{"id":34246,"date":"2023-09-22T05:35:35","date_gmt":"2023-09-22T05:35:35","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=34246"},"modified":"2024-02-05T16:17:22","modified_gmt":"2024-02-05T16:17:22","slug":"exponent-formulas-examples-facts-practice-problems-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/exponent-formulas","title":{"rendered":"Exponent Formulas &#8211;\u00a0 Examples, Facts, Practice Problems, FAQs"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-9ace1497-a39f-45d4-9ab3-17261cbb7018\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/exponent-formulas#0-what-are-exponent-formulas>What Are Exponent Formulas?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/exponent-formulas#1-exponent-formulas>Exponent Formulas<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/exponent-formulas#4-solved-examples-on-exponent-formulas>Solved Examples on Exponent Formulas<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/exponent-formulas#5-practice-problems-on-exponent-formulas>Practice Problems on Exponent Formulas<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/exponent-formulas#6-frequently-asked-questions-about-exponent-formulas>Frequently Asked Questions about Exponent Formulas<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-are-exponent-formulas\">What Are Exponent Formulas?<\/h2>\n\n\n\n<p><strong>The exponent formulas are mathematical rules that help you perform calculations and simplify expressions involving exponents more easily.&nbsp;<\/strong><\/p>\n\n\n\n<p>The exponent formulas represent the way to express a number raised to a certain power. It is written as <strong>Base<\/strong><strong><sup>Exponent<\/sup><\/strong> and signifies multiplying the base by itself the number of times indicated by the exponent.<\/p>\n\n\n\n<p><strong>Base and Exponent<\/strong>: The <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/base-of-an-exponent\">base of an exponent<\/a> is the number or letter you want to multiply, and the exponent tells you how many times to multiply it by itself.<\/p>\n\n\n\n<p>If you multiply the number \u201ca\u201d by itself n times, you can express this multiplication in a concise form using <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/exponent#:~:text=their%20various%20laws.-,The%20exponent%20of%20a%20number%20indicates%20the%20total%20time%20to,k%20to%208%20on%20SplashLearn.\">exponents<\/a>, instead of writing the number over and over again.<\/p>\n\n\n\n<p><strong>Example<\/strong>: Multiply 5 by itself three times.&nbsp;<\/p>\n\n\n\n<p>Instead of writing $5 \\times 5 \\times 5$, we can write 5<sup>3<\/sup>.&nbsp;<\/p>\n\n\n\n<p>So, 5 raised to the power of 3 means you&#8217;re multiplying 5 by itself three times: $5 \\times 5 \\times 5$, which equals 125.<\/p>\n\n\n\n<p>Here,&nbsp;<\/p>\n\n\n\n<p>5 is called the &#8220;<strong>base.<\/strong>&#8220;<\/p>\n\n\n\n<p>3 is called the &#8220;<strong>exponent<\/strong>&#8221; or &#8220;<strong>power.<\/strong>&#8220;<\/p>\n\n\n\n<p>5<sup>3<\/sup> is read as &#8220;<strong>5 to the power of 3<\/strong>&#8221; (or) &#8220;<strong>5 raised to 3.<\/strong>&#8221;&nbsp;<\/p>\n\n\n\n<p>The entire expression is called power.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"364\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/base-and-exponent.png\" alt=\"Base and exponent\" class=\"wp-image-34254\" title=\"Base and exponent\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/base-and-exponent.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/base-and-exponent-300x176.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Exponent formulas simplify calculations with repeated multiplication. They involve rules like product, quotient, power of a power, and fractional exponents, vital for various mathematical applications.<\/p>\n\n\n\n<p>These formulas offer a methodical technique to deal with numbers, variables, and exponent-based equations. When dealing with repeated components, they assist you in avoiding the need to carry out multiple multiplications.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"1-exponent-formulas\">Exponent Formulas<\/h2>\n\n\n\n<p>These formulas help to simplify expressions involving exponents. They involve rules for combining, separating, and simplifying terms with exponents.<\/p>\n\n\n\n<p>Take a look at the table given below to understand the various exponents formulas.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\"><strong>Rule<\/strong><\/th><th class=\"has-text-align-left\" data-align=\"left\"><strong>Description<\/strong><\/th><th class=\"has-text-align-left\" data-align=\"left\"><strong>Formula<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>Multiplication Rule&nbsp;<\/strong><strong>(Product of Powers Rule)<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">When you multiply numbers with the same base, add their exponents, keeping the same base.&nbsp;<\/td><td class=\"has-text-align-left\" data-align=\"left\">$a^{m} \\times a^{n} = a^{m+n}$<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><br><strong>Division Rule<\/strong><strong>(Power of Quotient Rule)<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">When you divide numbers with the same base, subtract their exponents, keeping the same base.&nbsp;<\/td><td class=\"has-text-align-left\" data-align=\"left\">$\\frac{a^{m}}{a^{n}} = a^{m-n} (a \\neq 0)$<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/power-of-a-power-rule\"><strong>Power of a Power Rule<\/strong><\/a><strong>&nbsp;<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">If the base raised to a power is being raised to another power, then the two powers are multiplied keeping the same base.<\/td><td class=\"has-text-align-left\" data-align=\"left\">$(a^{m})^{n} = a^{mn}$<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>Power of a Product Rule<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">To find the power of a product, find the power of each factor and then multiply.&nbsp;<\/td><td class=\"has-text-align-left\" data-align=\"left\">$(ab)^{m} = a^{m} \\times b^{m}$<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>Power of a Fraction Rule<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">When you have a fraction ab raised to an exponent m, you can raise both the numerator (a) and the denominator (b) to the power (m).&nbsp;<\/td><td class=\"has-text-align-left\" data-align=\"left\">$(\\frac{a}{b})^{m} = \\frac{a^{m}}{b^{m}} (b \\neq 0)$<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>Zero Exponent<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">Any nonzero base raised to the power of 0 equals 1.<\/td><td class=\"has-text-align-left\" data-align=\"left\">$a^{0} = 1$<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><br><strong>Negative Exponent<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">Negative exponents indicate reciprocals. when a number is raised to a negative exponent, we divide 1 by the base raised to a positive exponent.<\/td><td class=\"has-text-align-left\" data-align=\"left\">$a^{-m} = \\frac{1}{a^{m}}&nbsp;(a \\neq 0)$<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>Fractional Exponent<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">Exponents can also be fractional or rational numbers. The n<sup>th<\/sup> root of a number can be represented using fractional exponents.(a1nrepresents the nth root of a.)<\/td><td class=\"has-text-align-left\" data-align=\"left\">$a^{\\frac{m}{n}} = ^{n}\\sqrt{a_{m}}$<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/evaluate-expressions-involving-exponents\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/evaluate-expressions-involving-exponents.jpeg\" alt=\"Evaluate Expressions Involving Exponents Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"2-facts-about-exponent-formulas\">Facts about Exponent Formulas<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>Exponent formulas are rules that help us perform operations involving exponents more easily.<\/li>\n\n\n\n<li>A negative exponent in the denominator can be moved to the numerator as a positive exponent: $\\frac{1}{a^{-n}} = a^{n}$<\/li>\n\n\n\n<li>Exponential functions model processes that grow or decay rapidly. They are often used in contexts like population growth, compound interest, and radioactive decay.<\/li>\n\n\n\n<li>Logarithms can be used to simplify complex exponents. For instance, $log_{b}(a^{m}) = m \\times log_{b}(a)$.<\/li>\n\n\n\n<li>\u2061Exponents are used in geometry to calculate areas and volumes of shapes, such as the area of a circle $(A = \\pi r^{2})$ ot the volume of cube $(V = a^{3})$<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned about the exponent formulas. Exponents and powers formulas are essential tools in mathematics for simplifying and manipulating expressions involving powers and exponents. They provide a structured framework to work with numbers and variables raised to various powers. Now, let\u2019s understand exponent formulas better using a few solved examples and practice problems.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-solved-examples-on-exponent-formulas\">Solved Examples on Exponent Formulas<\/h2>\n\n\n\n<p><strong>Example 1: Simplify the following.&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>a. <\/strong>$3^{4} \\times 3^{2}$<strong>&nbsp;&nbsp;&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>b. <\/strong>$\\frac{x^{5}}{x^{3}}$<strong>&nbsp;&nbsp;&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>c. <\/strong>$5^{0}$<\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>a. $3^{4} \\times 3^{2}$<\/p>\n\n\n\n<p>Product of powers rule: $a^{m} \\times a^{n} = a^{m+n}$<\/p>\n\n\n\n<p>$3^{4} \\times 3^{2} = 3^{4 + 2} = 3^{6} =729$<\/p>\n\n\n\n<p>b. $\\frac{x{5}}{x^{3}}$<\/p>\n\n\n\n<p>Power of quotient rule: $\\frac{a^{m}}{a^{n}} = a^{m-n}$<\/p>\n\n\n\n<p>$\\frac{x^{5}}{x^{3}} = x^{5-3} = x^{2}$<\/p>\n\n\n\n<p>c. $5^{0}$<\/p>\n\n\n\n<p>Zero exponent rule: $a^{0} = 1$<\/p>\n\n\n\n<p>$5^{0} = 1$<\/p>\n\n\n\n<p><strong>Example 2: The dimensions of a rectangular box are <\/strong>$a^{4}$<strong> inches, <\/strong>$b^{3}$<strong> inches and a2 inches. Determine its volume.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>length (l) $= a^{4}$ inches<\/p>\n\n\n\n<p>width (w) $= b^{3}$ inches<\/p>\n\n\n\n<p>height (h) $= a^{2}$ inches<\/p>\n\n\n\n<p>Using the product of powers rule exponent formula, axay=ax+y<\/p>\n\n\n\n<p>Volume $= a^{4} \\times a^{2} \\times b^{3}$<\/p>\n\n\n\n<p>Volume $= a^{6} \\times b^{3}$<\/p>\n\n\n\n<p>The volume of the box is $a^{6} \\times b^{3}$.<\/p>\n\n\n\n<p><strong>Example 3: Simplify: <\/strong>$\\frac{y^{- \\frac{3}{4}}}{y^{\\frac{1}{4}}}$<\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>$\\frac{y^{-\\frac{3}{4}}{y^{\\frac{1}{4}}}$<\/p>\n\n\n\n<p>$= y^{- \\frac{3}{4} -\\frac{1}{4}}$<\/p>\n\n\n\n<p>$= y^{\\frac{-3-1}{4}}$<\/p>\n\n\n\n<p>$= y^{-1}$<\/p>\n\n\n\n<p>$= \\frac{1}{y}$<\/p>\n\n\n\n<p><strong>Example 4: If <\/strong>$2^{2x} = 32$<strong> and <\/strong>$3^{y} = 27$<strong>, find the value of x + y.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>First equation: $2^{2x} = 32$<\/p>\n\n\n\n<p>We can rewrite 32 as 2<sup>5<\/sup><\/p>\n\n\n\n<p>$2^{2x} = 2^{5}$<\/p>\n\n\n\n<p>Since the bases are the same (both are 2), we can equate the exponents.<\/p>\n\n\n\n<p>$2x = 5$<\/p>\n\n\n\n<p>$x = \\frac{5}{2}$<\/p>\n\n\n\n<p>Second equation: $3^{y} = 27$<\/p>\n\n\n\n<p>We can rewrite 27 as $3^{3}$.<\/p>\n\n\n\n<p>$3^{y} = 3^{3}$<\/p>\n\n\n\n<p>Again, we can equate the exponents since the base is equal.<\/p>\n\n\n\n<p>$y = 3$<\/p>\n\n\n\n<p>Now, let\u2019s find x + y<\/p>\n\n\n\n<p>$x + y = \\frac{5}{2} + 3 = \\frac{5 + 6}{2} = \\frac{11}{2}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-practice-problems-on-exponent-formulas\">Practice Problems on Exponent Formulas<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Exponent Formulas -\u00a0 Examples, Facts, Practice Problems, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">What does the Power of a Power Rule state?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">When multiplying numbers with different bases, add their exponents.<\/div><div class=\"spq_answer_block\" data-value=\"1\">When raising a power to another power, multiply the exponents.<\/div><div class=\"spq_answer_block\" data-value=\"2\">When dividing numbers with the same base, subtract their exponents.<\/div><div class=\"spq_answer_block\" data-value=\"3\">Any number raised to the power of 1 is equal to the number itself.<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: When raising a power to another power, multiply the exponents.<br\/>The Power of a Power Rule states that when a number raised to an exponent is again raised to another exponent, you multiply the exponents together.<br>\r\n$(a^{m})^{n} = a^{m \\times n}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What is $a^{0}$ equal to?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">1<\/div><div class=\"spq_answer_block\" data-value=\"1\">0<\/div><div class=\"spq_answer_block\" data-value=\"2\">a<\/div><div class=\"spq_answer_block\" data-value=\"3\">Undefined<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 1<br\/>According to the Power of Zero Rule, any nonzero number raised to the power of 0 is equal to 1.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">How can you simplify $a^{-3}$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$a^{3}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$-a^{3}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{1}{a^{3}}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$-\\frac{1}{a^{3}}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $\\frac{1}{a^{3}}$<br\/>According to the Negative Exponent Rule, we can write<br>\r\n$a^{-3} = \\frac{1}{a^{3}}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Which rule can be used to simplify $a^{m+n}$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Power of a Power Rule<\/div><div class=\"spq_answer_block\" data-value=\"1\">Product of Powers Rule<\/div><div class=\"spq_answer_block\" data-value=\"2\">Quotient of Powers Rule<\/div><div class=\"spq_answer_block\" data-value=\"3\">Negative Exponent Rule<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: Product of Powers Rule<br\/>The Product of Powers Rule is used to simplify expressions with the same base and different exponents. $a^{m} \u00d7 a^{n} = a^{m+n}$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">What is the result of $(\\frac{a}{b})^{2}$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{a^{2}}{b^{2}}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{a}{b^{2}}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{a^{2}}{b}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$a^{2}b^{2}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $\\frac{a^{2}}{b^{2}}$<br\/>The Power of a Fraction Rule states that $(\\frac{a}{b})^{2} = \\frac{a^{2}}{b^{2}}$<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Exponent Formulas -\u00a0 Examples, Facts, Practice Problems, FAQs\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Exponent Formulas\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What does the Power of a Power Rule state?\",\n                    \"text\": \"What does the Power of a Power Rule state?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The Power of a Power Rule states that when a number raised to an exponent is again raised to another exponent, you multiply the exponents together.<br>\r\n$$(a^{m})^{n} = a^{m \\\\times n}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"When multiplying numbers with different bases, add their exponents.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The Power of a Power Rule states that when a number raised to an exponent is again raised to another exponent, you multiply the exponents together.<br>\r\n$$(a^{m})^{n} = a^{m \\\\times n}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"When dividing numbers with the same base, subtract their exponents.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The Power of a Power Rule states that when a number raised to an exponent is again raised to another exponent, you multiply the exponents together.<br>\r\n$$(a^{m})^{n} = a^{m \\\\times n}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Any number raised to the power of 1 is equal to the number itself.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The Power of a Power Rule states that when a number raised to an exponent is again raised to another exponent, you multiply the exponents together.<br>\r\n$$(a^{m})^{n} = a^{m \\\\times n}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"When raising a power to another power, multiply the exponents.\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The Power of a Power Rule states that when a number raised to an exponent is again raised to another exponent, you multiply the exponents together.<br>\r\n$$(a^{m})^{n} = a^{m \\\\times n}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The Power of a Power Rule states that when a number raised to an exponent is again raised to another exponent, you multiply the exponents together.<br>\r\n$$(a^{m})^{n} = a^{m \\\\times n}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is $$a^{0}$$ equal to?\",\n                    \"text\": \"What is $$a^{0}$$ equal to?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"According to the Power of Zero Rule, any nonzero number raised to the power of 0 is equal to 1.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the Power of Zero Rule, any nonzero number raised to the power of 0 is equal to 1.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"a\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the Power of Zero Rule, any nonzero number raised to the power of 0 is equal to 1.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Undefined\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the Power of Zero Rule, any nonzero number raised to the power of 0 is equal to 1.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"1\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"According to the Power of Zero Rule, any nonzero number raised to the power of 0 is equal to 1.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"According to the Power of Zero Rule, any nonzero number raised to the power of 0 is equal to 1.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"How can you simplify $$a^{-3}$$?\",\n                    \"text\": \"How can you simplify $$a^{-3}$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"According to the Negative Exponent Rule, we can write<br>\r\n$$a^{-3} = \\\\frac{1}{a^{3}}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$a^{3}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the Negative Exponent Rule, we can write<br>\r\n$$a^{-3} = \\\\frac{1}{a^{3}}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$-a^{3}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the Negative Exponent Rule, we can write<br>\r\n$$a^{-3} = \\\\frac{1}{a^{3}}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$-\\\\frac{1}{a^{3}}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the Negative Exponent Rule, we can write<br>\r\n$$a^{-3} = \\\\frac{1}{a^{3}}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{1}{a^{3}}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"According to the Negative Exponent Rule, we can write<br>\r\n$$a^{-3} = \\\\frac{1}{a^{3}}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"According to the Negative Exponent Rule, we can write<br>\r\n$$a^{-3} = \\\\frac{1}{a^{3}}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which rule can be used to simplify $$a^{m+n}$$?\",\n                    \"text\": \"Which rule can be used to simplify $$a^{m+n}$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The Product of Powers Rule is used to simplify expressions with the same base and different exponents. $$a^{m} \u00d7 a^{n} = a^{m+n}$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Power of a Power Rule\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The Product of Powers Rule is used to simplify expressions with the same base and different exponents. $$a^{m} \u00d7 a^{n} = a^{m+n}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Quotient of Powers Rule\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The Product of Powers Rule is used to simplify expressions with the same base and different exponents. $$a^{m} \u00d7 a^{n} = a^{m+n}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Negative Exponent Rule\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The Product of Powers Rule is used to simplify expressions with the same base and different exponents. $$a^{m} \u00d7 a^{n} = a^{m+n}$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Product of Powers Rule\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The Product of Powers Rule is used to simplify expressions with the same base and different exponents. $$a^{m} \u00d7 a^{n} = a^{m+n}$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The Product of Powers Rule is used to simplify expressions with the same base and different exponents. $$a^{m} \u00d7 a^{n} = a^{m+n}$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the result of $$(\\\\frac{a}{b})^{2}$$?\",\n                    \"text\": \"What is the result of $$(\\\\frac{a}{b})^{2}$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The Power of a Fraction Rule states that $$(\\\\frac{a}{b})^{2} = \\\\frac{a^{2}}{b^{2}}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{a}{b^{2}}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The Power of a Fraction Rule states that $$(\\\\frac{a}{b})^{2} = \\\\frac{a^{2}}{b^{2}}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{a^{2}}{b}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The Power of a Fraction Rule states that $$(\\\\frac{a}{b})^{2} = \\\\frac{a^{2}}{b^{2}}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$a^{2}b^{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The Power of a Fraction Rule states that $$(\\\\frac{a}{b})^{2} = \\\\frac{a^{2}}{b^{2}}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{a^{2}}{b^{2}}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The Power of a Fraction Rule states that $$(\\\\frac{a}{b})^{2} = \\\\frac{a^{2}}{b^{2}}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The Power of a Fraction Rule states that $$(\\\\frac{a}{b})^{2} = \\\\frac{a^{2}}{b^{2}}$$\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-frequently-asked-questions-about-exponent-formulas\">Frequently Asked Questions about Exponent Formulas<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-d1f4c961-2e77-445d-934b-79c4eb000446\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-d1f4c961-2e77-445d-934b-79c4eb000446\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-d1f4c961-2e77-445d-934b-79c4eb000446\"><strong>What is an exponent, and how is it represented in mathematical notation?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-d1f4c961-2e77-445d-934b-79c4eb000446\">\n\n<p>An exponent is a small number placed above and to the right of a base number, indicating how many times the base is multiplied by itself. It&#8217;s represented as &#8220;base<sup>exponent<\/sup>.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-d1f4c961-2e77-445d-934b-79c4eb000446\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-d1f4c961-2e77-445d-934b-79c4eb000446\"><strong>What is the difference between an exponent and a base in an exponent formula?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-d1f4c961-2e77-445d-934b-79c4eb000446\">\n\n<p>The base is the number being raised to a certain power, while the exponent is the small number indicating how many times the base is multiplied by itself.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-d1f4c961-2e77-445d-934b-79c4eb000446\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-d1f4c961-2e77-445d-934b-79c4eb000446\"><strong>What is the meaning of a positive exponent in an exponent formula?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-d1f4c961-2e77-445d-934b-79c4eb000446\">\n\n<p>A positive exponent indicates how many times the base is multiplied by itself. For example, $2^{3} = 2 \\times 2 \\times 2 = 8$<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-d1f4c961-2e77-445d-934b-79c4eb000446\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-d1f4c961-2e77-445d-934b-79c4eb000446\"><strong>What does a negative exponent signify in an exponent formula?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-d1f4c961-2e77-445d-934b-79c4eb000446\">\n\n<p>A negative exponent indicates that the base is in the denominator of a fraction. For example, $2^{-3} = \\frac{1}{2^{3}} = \\frac{1}{8}$<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-d1f4c961-2e77-445d-934b-79c4eb000446\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-d1f4c961-2e77-445d-934b-79c4eb000446\"><strong>Can exponent formulas be used with negative bases?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-d1f4c961-2e77-445d-934b-79c4eb000446\">\n\n<p>Yes, exponent formulas work with negative bases as well. The rules apply regardless of whether the base is positive or negative.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Are Exponent Formulas? The exponent formulas are mathematical rules that help you perform calculations and simplify expressions involving exponents more easily.&nbsp; The exponent formulas represent the way to express a number raised to a certain power. It is written as BaseExponent and signifies multiplying the base by itself the number of times indicated by &#8230; <a title=\"Exponent Formulas &#8211;\u00a0 Examples, Facts, Practice Problems, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/exponent-formulas\" aria-label=\"More on Exponent Formulas &#8211;\u00a0 Examples, Facts, Practice Problems, FAQs\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-34246","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/34246","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=34246"}],"version-history":[{"count":8,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/34246\/revisions"}],"predecessor-version":[{"id":39971,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/34246\/revisions\/39971"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=34246"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=34246"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=34246"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}