{"id":1060,"date":"2022-04-13T12:06:14","date_gmt":"2022-04-13T12:06:14","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test-new\/?page_id=1060"},"modified":"2024-03-15T08:36:56","modified_gmt":"2024-03-15T08:36:56","slug":"exponent-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/exponent","title":{"rendered":"Exponent &#8211; Definition with Examples"},"content":{"rendered":"\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\"><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-761b0012-2692-4d63-a8f4-4c7dea309932\" 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\/algebra\/exponent#0-definition-of-exponent>Definition of Exponent<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/exponent#3-properties-of-exponent->Properties of Exponent&nbsp;<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/exponent#5-solved-examples->Solved Examples&nbsp;<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/exponent#6-practice-problems>Practice Problems<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/exponent#7-frequently-asked-questions>Frequently Asked Questions<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-definition-of-exponent\">Definition of Exponent<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The exponent of a number indicates the total time to use that number in a multiplication. For example, 8 \u00d7 8 \u00d7 8&nbsp; can be expressed as 8<sup>3<\/sup> because 8 is multiplied by itself 3 times. Here, 3 is the \u2018exponent\u2019 or \u2018power\u2019 which tells how many times 8 is multiplied by itself, and 8 is the \u2018base\u2019 which represents the number being multiplied. In short, power or exponent indicates the number of times a number needs to be multiplied by itself. Here, the base can be any integer, fraction or decimal. The exponent can also take up any value, be it positive or negative.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"346\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/example-of-exponent-and-base-number.png\" alt=\"Example of Exponent and Base Number\" class=\"wp-image-41018\" title=\"Example of Exponent and Base Number\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/example-of-exponent-and-base-number.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/example-of-exponent-and-base-number-300x167.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/evaluate-algebraic-expressions-with-one-operation\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/algebra_evaluate_algebric_exp_1_pt.png\" alt=\"Evaluate Algebraic Expressions with One Operation Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Evaluate Algebraic Expressions with One Operation Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/evaluate-algebraic-expressions-with-two-operations\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/algebra_evaluate_algebric_exp_2_pt.png\" alt=\"Evaluate Algebraic Expressions with Two Operations Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Evaluate Algebraic Expressions with Two Operations Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/form-algebraic-expressions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/algebra_choose_exp_1_pt.png\" alt=\"Form Algebraic Expressions Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Form Algebraic Expressions Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-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 eplus-wrapper\" id=\"1-examples-of-exponent\">Examples of Exponent<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Here are some examples:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">5<sup>4<\/sup> = 5 \u00d7 5 \u00d7 5 \u00d7 5 = 625&nbsp;<\/li>\n\n\n\n<li class=\"eplus-wrapper\">3<sup>5<\/sup> = 3 \u00d7 3 \u00d7 3 \u00d7 3 \u00d7 3 = 243<\/li>\n\n\n\n<li class=\"eplus-wrapper\">14<sup>2<\/sup> = 14 \u00d7 14 = 196<\/li>\n\n\n\n<li class=\"eplus-wrapper\">(\u22124)<sup>3<\/sup> = (\u22124) \u00d7 (\u22124) \u00d7 (\u22124) = \u221264<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$\\left(\\frac{1}{2} \\right)^{4}$ = $\\left(\\frac{1}{2} \\right)\\times \\left(\\frac{1}{2} \\right)\\times \\left(\\frac{1}{2} \\right)\\times \\left(\\frac{1}{2} \\right)$ =&nbsp; $\\frac{1}{16}$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">(0.2)<sup>3<\/sup> = 0.2 \u00d7 0.2 \u00d7 0.2 = 0.008<\/li>\n<\/ul>\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 eplus-wrapper\" id=\"2-how-to-read-numbers-with-exponents\">How to Read Numbers with Exponents<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">$x^{n}$ can be read in many ways.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">x to the power of n<\/li>\n\n\n\n<li class=\"eplus-wrapper\">x raised to n<\/li>\n\n\n\n<li class=\"eplus-wrapper\">x to the n<\/li>\n\n\n\n<li class=\"eplus-wrapper\">x to the nth power<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">There are some special cases:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x^{2}$ is also read as x square and $x^{3}$ is also read as x cube.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"374\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/read-numbers-with-exponents.png\" alt=\"Read Numbers with Exponents\" class=\"wp-image-41019\" title=\"Read Numbers with Exponents\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/read-numbers-with-exponents.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/read-numbers-with-exponents-300x181.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-properties-of-exponent-\">Properties of Exponent&nbsp;<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The rules or properties of exponents are used widely to solve various problems. Let us learn about them one by one:&nbsp;<\/p>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Law of product&nbsp;<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\">As per the law, to find the product of exponential expressions with the same base we add the exponents. It is given as:&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;a<sup>m<\/sup> \u00d7 a<sup>n<\/sup> = a<sup>m + n<\/sup>, where m and n are real numbers<\/p>\n\n\n\n<ol start=\"2\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Law of quotient&nbsp;<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\">As per the law, to divide two exponential expression with the same base we subtract the exponents. It is given as:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;$\\frac{a^{m}}{a^{n}}$ = a<sup>m \u2013 n<\/sup>, where m and n are real numbers and a is a non-zero term.<\/p>\n\n\n\n<ol start=\"3\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Law of negative exponent&nbsp;<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\">The negative exponent rule states that when an exponent is negative, we can convert it into positive by reciprocating it. It is represented as:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">a<sup>\u2013m<\/sup> = $\\frac{1}{a^{m}}$, where a is a non-zero number and m is a real number.<br><\/p>\n\n\n\n<ol start=\"4\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Law of zero exponent&nbsp;<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\">As per this law, if the exponent of a real number is 0, then its value is equal to 1, as<\/p>\n\n\n\n<p class=\"eplus-wrapper\">a<sup>0<\/sup> = 1.<\/p>\n\n\n\n<ol start=\"5\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Law of power of a product&nbsp;<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\">As per this law, multiplying two different bases with the same power is equal to the product of the base with the power. For instance,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">a<sup>n<\/sup> b<sup>n<\/sup> = (ab)<sup>n<\/sup><\/p>\n\n\n\n<ol start=\"6\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Law of power of a power&nbsp;<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\">As per this law, when the power raised to the another power of a base we multiply the exponents. It is represented as:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">(a<sup>m <\/sup>)<sup>n<\/sup> = a<sup>mn<\/sup><\/p>\n\n\n\n<ol start=\"7\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Law of power of a quotient&nbsp;<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\">According to this law, the division of different bases with the same power is represented as<\/p>\n\n\n\n<p class=\"eplus-wrapper\">a$\\frac{a^{n}}{b^{n}}$ = $\\left (\\frac{a}{b}\\right)^n$, where b is non-zero term.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Your child must be good at multiplication to solve exponents quickly, so make your child learn multiplication and various other mathematical concepts with ease through SplashLearn <a href=\"https:\/\/www.splashlearn.com\/math\/multiplication-worksheets\">Worksheets<\/a> and various <a href=\"https:\/\/www.splashlearn.com\/tutoring\/courses\">Tutoring Courses<\/a> for kids of Grades Pre-k to 5.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-fun-facts\">Fun Facts<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">A base with 0 as its power is always equal to 1.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Any number raised to power 1 is always equal to that number.&nbsp;<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Any power raised to the base 0 is always equal to 0.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The history of power or exponent is quite old. The term was used for the first time in 1544.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-solved-examples-\">Solved Examples&nbsp;<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 1: Evaluate 7<\/strong><strong><sup>3&nbsp;<\/sup><\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>&nbsp;Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">7<sup>3 <\/sup>= 7 \u00d7 7 \u00d7 7 = 343<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 2: Express the result in exponential form.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>2<\/strong><strong><sup>3<\/sup><\/strong><strong> \u00d7 2<\/strong><strong><sup>4<\/sup><\/strong><strong> \u00d7 2<\/strong><strong><sup>7<\/sup><\/strong><strong> \u00d7 2<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">2<sup>3<\/sup> \u00d7 2<sup>4<\/sup> \u00d7 2<sup>7<\/sup> \u00d7 2 = 2<sup>3 + 4 + 7 + 1<\/sup> = 2<sup>15<\/sup><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Example 3: Simplify $\\Bigg\\{\\Big(\\frac{2}{3}\\Big)^{3}\\Bigg\\}^{-2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Bigg\\{\\Big(\\frac{2}{3}\\Big)^{3}\\Bigg\\}^{-2}$ = $\\frac{2}{3}^{-6}$ = $\\frac{3}{2}^{6}$ = $\\frac{729}{64}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 4: Simplify the following<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">(i) 2<sup>12<\/sup> \u00f7 2<sup>5<\/sup><\/p>\n\n\n\n<p class=\"eplus-wrapper\">(ii) 3<sup>3 <\/sup>\u00d7 4<sup>3<\/sup><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">(i) 2<sup>12<\/sup> \u00f7 2<sup>5 <\/sup>= 2<sup>12 \u2013 5<\/sup> = 2<sup>7<\/sup>= 128.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">(ii) 3<sup>3 <\/sup>\u00d7 4<sup>3 <\/sup>= (3 \u00d7 4)<sup> 3<\/sup> = 1728<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-conclusion-\">Conclusion&nbsp;<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In this article, we have learnt about exponents and their various laws. The exponent of a number indicates the total time to use that number in a multiplication. They are important to write the values of numbers in simplified form.<br>Read more about exponents and other interesting mathematical terms for children in grades Pre-k to 8 on <a href=\"https:\/\/www.splashlearn.com\/\">SplashLearn<\/a>.\u00a0<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-practice-problems\">Practice Problems<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Exponent<\/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 is the value of (\u20133)<sup>3<\/sup>?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">27<\/div><div class=\"spq_answer_block\" data-value=\"1\">-27<\/div><div class=\"spq_answer_block\" data-value=\"2\">24<\/div><div class=\"spq_answer_block\" data-value=\"3\">-24<\/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: -27<br\/>$ \u22123  \u00d7 \u22123  \u00d7 \u22123 = \u221227$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What is the simplified answer of 4<sup>0<\/sup> \u2013 2<sup>0<\/sup>?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">1<\/div><div class=\"spq_answer_block\" data-value=\"1\">0<\/div><div class=\"spq_answer_block\" data-value=\"2\">-1<\/div><div class=\"spq_answer_block\" data-value=\"3\">2<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 0<br\/>4<sup>0<\/sup> \u2013 2<sup>0<\/sup> = 1 \u2013 1 = 0<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">$\\frac{5^{4}}{5^{2}}$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">24<\/div><div class=\"spq_answer_block\" data-value=\"1\">23<\/div><div class=\"spq_answer_block\" data-value=\"2\">19<\/div><div class=\"spq_answer_block\" data-value=\"3\">25<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 25<br\/>$\\frac{5^{4}}{5^{2}} = {5^{4 - 2}} = {5^{2}} = 25$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Simplify: $4^{\u22122}$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">0.0625<\/div><div class=\"spq_answer_block\" data-value=\"1\">0.625<\/div><div class=\"spq_answer_block\" data-value=\"2\">0.624 <\/div><div class=\"spq_answer_block\" data-value=\"3\">0.0624<\/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: 0.0625<br\/>$4^{\u22122}$ = $\\frac{1}{4^{2}}$ = 0.0625<\/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\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Exponent\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the value of (\u20133)<sup>3<\/sup>?\",\n                    \"text\": \"What is the value of (\u20133)<sup>3<\/sup>?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$ \u22123  \u00d7 \u22123  \u00d7 \u22123 = \u221227$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"27\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$ \u22123  \u00d7 \u22123  \u00d7 \u22123 = \u221227$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"24\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$ \u22123  \u00d7 \u22123  \u00d7 \u22123 = \u221227$$\"\n                                    }\n                    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  \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$ \u22123  \u00d7 \u22123  \u00d7 \u22123 = \u221227$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the simplified answer of 4<sup>0<\/sup> \u2013 2<sup>0<\/sup>?\",\n                    \"text\": \"What is the simplified answer of 4<sup>0<\/sup> \u2013 2<sup>0<\/sup>?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"4<sup>0<\/sup> \u2013 2<sup>0<\/sup> = 1 \u2013 1 = 0\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n 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       \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"4<sup>0<\/sup> \u2013 2<sup>0<\/sup> = 1 \u2013 1 = 0\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"0\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"4<sup>0<\/sup> \u2013 2<sup>0<\/sup> = 1 \u2013 1 = 0\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"4<sup>0<\/sup> \u2013 2<sup>0<\/sup> = 1 \u2013 1 = 0\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"$$\\\\frac{5^{4}}{5^{2}}$$\",\n                    \"text\": \"$$\\\\frac{5^{4}}{5^{2}}$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$\\\\frac{5^{4}}{5^{2}} = {5^{4 - 2}} = {5^{2}} = 25$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"24\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{5^{4}}{5^{2}} = {5^{4 - 2}} = {5^{2}} = 25$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"23\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{5^{4}}{5^{2}} = {5^{4 - 2}} = {5^{2}} = 25$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"19\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{5^{4}}{5^{2}} = {5^{4 - 2}} = {5^{2}} = 25$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"25\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$\\\\frac{5^{4}}{5^{2}} = {5^{4 - 2}} = {5^{2}} = 25$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$\\\\frac{5^{4}}{5^{2}} = {5^{4 - 2}} = {5^{2}} = 25$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Simplify: $$4^{\u22122}$$\",\n                    \"text\": \"Simplify: $$4^{\u22122}$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$4^{\u22122}$$ = $$\\\\frac{1}{4^{2}}$$ = 0.0625\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0.625\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$4^{\u22122}$$ = $$\\\\frac{1}{4^{2}}$$ = 0.0625\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0.624 \",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$4^{\u22122}$$ = $$\\\\frac{1}{4^{2}}$$ = 0.0625\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0.0624\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$4^{\u22122}$$ = $$\\\\frac{1}{4^{2}}$$ = 0.0625\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"0.0625\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$4^{\u22122}$$ = $$\\\\frac{1}{4^{2}}$$ = 0.0625\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$4^{\u22122}$$ = $$\\\\frac{1}{4^{2}}$$ = 0.0625\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-frequently-asked-questions\">Frequently Asked Questions<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-8643362b-827a-42cd-99ec-46b68975eccc\" 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-0-8643362b-827a-42cd-99ec-46b68975eccc\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8643362b-827a-42cd-99ec-46b68975eccc\"><strong>What are the real-life applications of exponent?<\/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-0-8643362b-827a-42cd-99ec-46b68975eccc\">\n\n<p>Exponents have various applications. A few of them are mentioned below:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Scientific scales like the Richter scale and Ph scale are based on exponents.&nbsp;<\/li>\n\n\n\n<li>They are widely used to calculate volume, area, and measurement-related problems.<\/li>\n\n\n\n<li>They are also used in computer games.<\/li>\n<\/ul>\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-1-8643362b-827a-42cd-99ec-46b68975eccc\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8643362b-827a-42cd-99ec-46b68975eccc\"><strong>What is the importance of exponent?<\/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-1-8643362b-827a-42cd-99ec-46b68975eccc\">\n\n<p>Exponents are important to write the values of numbers in simplified form. Repeated multiplication can be simply written with the help of exponents.<\/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-2-8643362b-827a-42cd-99ec-46b68975eccc\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8643362b-827a-42cd-99ec-46b68975eccc\"><strong>What are zero exponents?<\/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-2-8643362b-827a-42cd-99ec-46b68975eccc\">\n\n<p>Zero exponents are the numbers with 0 as their exponent. Any base with 0 as its exponent is equal to 1.<\/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-3-8643362b-827a-42cd-99ec-46b68975eccc\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8643362b-827a-42cd-99ec-46b68975eccc\"><strong>When can exponents be added?<\/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-3-8643362b-827a-42cd-99ec-46b68975eccc\">\n\n<p>When exponents with the same base are multiplied, we can add their powers.<\/p>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Definition of Exponent The exponent of a number indicates the total time to use that number in a multiplication. For example, 8 \u00d7 8 \u00d7 8&nbsp; can be expressed as 83 because 8 is multiplied by itself 3 times. Here, 3 is the \u2018exponent\u2019 or \u2018power\u2019 which tells how many times 8 is multiplied by &#8230; <a title=\"Exponent &#8211; Definition with Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/exponent\" aria-label=\"More on Exponent &#8211; Definition with Examples\">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-1060","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\/1060","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=1060"}],"version-history":[{"count":21,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1060\/revisions"}],"predecessor-version":[{"id":41022,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1060\/revisions\/41022"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=1060"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=1060"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=1060"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}