{"id":32643,"date":"2023-08-06T17:44:55","date_gmt":"2023-08-06T17:44:55","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=32643"},"modified":"2023-08-07T02:38:10","modified_gmt":"2023-08-07T02:38:10","slug":"power-of-a-power-rule-definition-rules-examples-facts-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/power-of-a-power-rule","title":{"rendered":"Power of a Power Rule: Definition, Rules, Examples, Facts, 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-42f4587f-417f-4739-bed9-63a4e0e1c596\" 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\/power-of-a-power-rule#0-what-is-the-power-of-a-power-rule>What Is the Power of a Power Rule?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/power-of-a-power-rule#1-power-of-a-power-rule-with-negative-exponents>Power of a Power Rule with Negative Exponents<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/power-of-a-power-rule#3-simplifying-expressions-the-power-of-a-power-rule>Simplifying Expressions the Power of a Power Rule<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/power-of-a-power-rule#6-solved-examples-on-power-of-a-power-rule>Solved Examples on Power of a Power Rule<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/power-of-a-power-rule#7-practice-problems-on-the-power-of-a-power-rule>Practice Problems on the Power of a Power Rule<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/power-of-a-power-rule#8-frequently-asked-questions-on-the-power-of-a-power-rule>Frequently Asked Questions on the Power of a Power Rule<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-the-power-of-a-power-rule\">What Is the Power of a Power Rule?<\/h2>\n\n\n\n<p>The<strong> power of a power rule <\/strong>is an important <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/exponent\">exponent<\/a> rule (law of exponent) used to simplify an expression of the form $(x^{m})^{n}$, where the base x is raised to a power m and the entire expression $x^{m}$ is raised to the power n again.\u00a0<\/p>\n\n\n\n<p><strong>Power raised to a power rule<\/strong> is given by<\/p>\n\n\n\n<p>$(x^{m})^{n} = x^{m \\times n} = x^{mn}$ \u2026where x is the base, m and n are exponents<\/p>\n\n\n\n<p>This means that if a base is raised to power and on the whole <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/term\">term<\/a> raised to another power, then the two powers are multiplied, keeping the same base.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$x^{m}$ means that the base \u201cx\u201d is multiplied by itself\u00a0 \u201cm\u201d times.\u00a0<\/li>\n\n\n\n<li>$(x^{m})^{n}$ means that the base $(x^{m})$ is multiplied by itself \u201cn\u201d times.<\/li>\n\n\n\n<li>$x^{mn}$ means the base \u201cx\u201d is multiplied by itself\u00a0 \u201cmn\u201d times.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"433\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/power-of-a-power-rule.png\" alt=\"Power of a power rule\" class=\"wp-image-32651\" title=\"Power of a power rule\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/power-of-a-power-rule.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/power-of-a-power-rule-300x210.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p><strong>Power of a power rule examples:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$(a^{2})^{3} = a^{2 \u00d7 3} = a^{6}$<\/li>\n\n\n\n<li>$(2^{4})^{2} = 2^{4 \u00d7 2} = 2^{8}$<\/li>\n\n\n\n<li>$\\left[(p + q)^{5}\\right]^{7} = (p + q)^{5 \u00d7 7} = (p + q)^{35}$<\/li>\n\n\n\n<li>$\\left[(\\;-\\;1)^{4}\\right]^{2} = (\\;-\\;1)^{4 \u00d7 2} =\u00a0 (-1)^{8} = 1$<\/li>\n<\/ul>\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\/divide-the-decimal-by-power-of-10\" 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\/dec_mul_div_div_power_10_1_pt.png\" alt=\"Divide the Decimal by Power of 10 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\">Divide the Decimal by Power of 10 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\/generate-patterns-from-the-rule\" 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_generate_patterns_pt.png\" alt=\"Generate Patterns from the Rule 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\">Generate Patterns from the Rule 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\/identify-the-correct-rule-of-pattern-used\" 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_guess_rule_2_pt.png\" alt=\"Identify the Correct Rule of Pattern Used 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\">Identify the Correct Rule of Pattern Used 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\/identify-the-rule-of-the-pattern\" 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_guess_rule_pattern_pt.png\" alt=\"Identify the Rule of the Pattern 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\">Identify the Rule of the Pattern 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\/measure-lengths-on-a-ruler-by-subtracting\" 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\/measurement_length_ruler_sub_pt.png\" alt=\"Measure Lengths on a Ruler by Subtracting 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\">Measure Lengths on a Ruler by Subtracting 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\/multiply-by-power-of-10\" 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\/dec_mul_div_multiply_by_power_10_2_pt.png\" alt=\"Multiply by Power of 10 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\">Multiply by Power of 10 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\/multiply-the-decimal-numbers-by-a-power-of-10\" 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\/dec_mul_div_multiply_by_power_10_1_pt.png\" alt=\"Multiply the Decimal Numbers by a Power of 10 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\">Multiply the Decimal Numbers by a Power of 10 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\/perform-division-with-powers-of-10-as-divisors\" 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\/dec_mul_div_div_power_10_2_pt.png\" alt=\"Perform Division With Powers of 10 as Divisors 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\">Perform Division With Powers of 10 as Divisors 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                   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      checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"1-power-of-a-power-rule-with-negative-exponents\">Power of a Power Rule with Negative Exponents<\/h2>\n\n\n\n<p>When we are dealing with the negative exponents, we have to also apply the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/multiplication\">multiplication<\/a> rules used with respect to the negative sign.&nbsp;<\/p>\n\n\n\n<p>Note that $x^{-\\;n} = \\frac{1}{x^{n}}$.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$(a^{-\\;m})^{-\\;n} = a^{-\\;m \u00d7\\;-\\; n} = a^{mn}$<\/li>\n\n\n\n<li>$(a^{-\\;m})^{n} = a^{-\\;m \u00d7 n} = a^{-\\;mn} = \\frac{1}{a^{mn}}$<\/li>\n\n\n\n<li>$(a^{m})^{-\\;n} = a^{m \u00d7 \\;-\\;n} = a^{-\\;mn}$<\/li>\n\n\n\n<li>$(x^{-\\;m})^{-\\;n} = x^{-\\;m \u00d7\\;-\\;n} = x^{mn}$<\/li>\n<\/ul>\n\n\n\n<p><strong>Examples:&nbsp;<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$(2^{-\\;2})^{-\\;3} = (2)^{-\\;2 \u00d7 \\;-\\;3} = 2^{6} = 64$<\/li>\n\n\n\n<li>$(x^{-\\;m})^{n} = x^{-\\;m \u00d7 n} = x^{-\\;mn} = \\frac{1}{x^{mn}}$<\/li>\n\n\n\n<li>$(2^{2})^{-\\;3} = (2)^{2 \u00d7 \\;-\\;3} = 2^{-\\;6} = 164$<\/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\/decode-the-code-powers-of-10\" 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\/decode-the-code-powers-of-10.jpeg\" alt=\"Decode the Code\u2014 Powers of 10 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 class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/divide-decimals-by-powers-of-10-horizontal-division\" 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\/divide-decimals-by-powers-of-10-horizontal-division.jpeg\" alt=\"Divide Decimals by Powers of 10: Horizontal Division 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 class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/divide-decimals-by-powers-of-10-horizontal-timed-practice\" 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\/divide-decimals-by-powers-of-10-horizontal-timed-practice.jpeg\" alt=\"Divide Decimals by Powers of 10: Horizontal Timed Practice\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/divide-decimals-by-powers-of-10-missing-numbers\" data-vars-ga-category=\"splashlearn_vocab\" 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src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/divide-hundredths-by-powers-of-10-horizontal-division.jpeg\" alt=\"Divide Hundredths by Powers of 10: Horizontal Division 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 class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/divide-hundredths-by-powers-of-10-missing-numbers\" 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\/divide-hundredths-by-powers-of-10-missing-numbers.jpeg\" alt=\"Divide Hundredths by Powers of 10: Missing Numbers 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 class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/divide-tenths-by-powers-of-10-horizontal-division\" 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\/divide-tenths-by-powers-of-10-horizontal-division.jpeg\" alt=\"Divide Tenths by Powers of 10: Horizontal Division 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 class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/divide-tenths-by-powers-of-10-missing-numbers\" 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\/divide-tenths-by-powers-of-10-missing-numbers.jpeg\" alt=\"Divide Tenths by Powers of 10: Missing Numbers 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 class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/identify-the-rule-of-the-given-number-pattern\" 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\/identify-the-rule-of-the-given-number-pattern.jpeg\" alt=\"Identify the Rule of the Given Number Pattern 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 class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/measure-length-using-ruler\" 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\/measure-length-using-ruler.jpeg\" alt=\"Measure Length Using Ruler 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-fraction-power-to-power-rule\">Fraction Power to Power Rule<\/h2>\n\n\n\n<p>Let\u2019s understand the power to a <strong>power rule of exponents<\/strong> when the exponent is a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/fraction\">fraction<\/a>.\u00a0<br>In this case, the two <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/denominator\">denominators<\/a> and <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/division\/numerator\">numerators<\/a> are multiplied.<\/p>\n\n\n\n<p>The formula can be written as<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$(x^{\\frac{m}{n}})^{\\frac{p}{q}} = x^{\\frac{pm}{qn}}$<\/li>\n\n\n\n<li>$(x^{m})^{\\frac{p}{q}} = x^{\\frac{pm}{q}}$<\/li>\n\n\n\n<li>$(x^{\\frac{m}{n}})^{p} = x^{\\frac{pm}{n}}$<\/li>\n<\/ul>\n\n\n\n<p>Let us see some examples of rational power of a power rule to understand better:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$(x^{\\frac{1}{2}})^{4} = x^{\\frac{1}{2} \u00d7 4} = x^{2}$<\/li>\n\n\n\n<li>$(2^{\\frac{3}{2}})^{\\frac{2}{3}} = 2^{\\frac{3}{2} \u00d7 \\frac{2}{3}} = 2^{1} = 2$<\/li>\n\n\n\n<li>$(3^{-\\;2})^{\\frac{3}{2}} = 3^{-\\;2 \u00d7 \\frac{3}{2}} = 3^{-\\;3} = \\frac{1}{3^{3}}$<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-simplifying-expressions-the-power-of-a-power-rule\">Simplifying Expressions the Power of a Power Rule<\/h2>\n\n\n\n<p>Let\u2019s simplify an expression using the power of a power rule.<\/p>\n\n\n\n<p><strong>Example: <\/strong>Find the value of $\\left[(\\;-\\;3)^{2}\\right]^{3}$.<\/p>\n\n\n\n<p>To simplify the expression $(\\;-\\;3^{2})^{3}$, we have to apply the power to the power rule, because the base is raised to a power and the whole is raised to another power. So we have to multiply the powers 2 and 3 to simplify this expression.<\/p>\n\n\n\n<p>$\\left[(\\;-\\;3)^{2}\\right]^{3}$<\/p>\n\n\n\n<p>$= (\\;-\\;3)^{2 \u00d7 3}$<\/p>\n\n\n\n<p>$=(\\;-\\;3)^{6}$<\/p>\n\n\n\n<p>$= (\\;-\\;3) \u00d7 (\\;-\\;3) \u00d7 (\\;-\\;3) \u00d7 (\\;-\\;3) \u00d7 (\\;-\\;3) \u00d7 (\\;-\\;3)$<\/p>\n\n\n\n<p>$= 729$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-facts-about-power-of-a-power-rule\">Facts about Power of a Power Rule<\/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>The power of a power rule can be used if the base is raised to a power and the whole term is again raised to another power. The two powers can be multiplied without changing the base.<\/li>\n\n\n\n<li>Power of a power rule formula: $(a^{m})^{n} = a^{mn}$<\/li>\n\n\n\n<li>Any non-zero base raised to the power 0 is 1.<\/li>\n\n\n\n<li>Power of a power rule is also termed as power to a power rule.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-conclusion\"><br>Conclusion<\/h2>\n\n\n\n<p>In this article, we have learned the power of a power rule and its formula in detail. We have also understood the application of the power of a power rule in simplifying expressions with negative and rational exponents. Now let us solve and practice the rule with a few examples.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-solved-examples-on-power-of-a-power-rule\">Solved Examples on Power of a Power Rule<\/h2>\n\n\n\n<p><strong>1. Identify the value of <\/strong>$(5^{2})^{2}$<strong>.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given expression: $(5^{2})^{2}$<\/p>\n\n\n\n<p>The power of a power formula is, $(a^{m})^{n} = a^{mn}$<\/p>\n\n\n\n<p>Let us multiply both the powers,<\/p>\n\n\n\n<p>$(5^{2})^{2} = 5^{2 \u00d7 2} = 5^{4}$<\/p>\n\n\n\n<p>Now solve the expression<\/p>\n\n\n\n<p>$5^{4} = 5 \u00d7 5 \u00d7 5 \u00d7 5$<\/p>\n\n\n\n<p>$5^{4} = 625$<\/p>\n\n\n\n<p>Thus the value of the expression <strong>\u00a0<\/strong>$(5^{2})^{2}$ is 625.<\/p>\n\n\n\n<p><strong>2. Find the value of <\/strong>$\\left[(\\;-\\;3)^{-\\;3}\\right]{-\\;2}$.<\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given expression: $\\left[(\\;-\\;3)^{-\\;3}\\right]^{-\\;2}$<\/p>\n\n\n\n<p>By using the power of a power formula, $(a^{-\\;m})^{-\\;n} = a^{-\\;m \u00d7 \\;-\\;n} = a^{mn}$<\/p>\n\n\n\n<p>Let&#8217;s solve the expression.<\/p>\n\n\n\n<p>$\\left[(\\;-\\;3)^{-\\;3}\\right]^{-\\;2}$<\/p>\n\n\n\n<p>$= (\\;-\\;3)^{-\\;3 \u00d7 \\;-\\;2}$<\/p>\n\n\n\n<p>$= (\\;-\\;3)^{6}$<\/p>\n\n\n\n<p>$= 729$<\/p>\n\n\n\n<p>Thus the value of the expression $\\left[(\\;-\\;3)^{-\\;3}\\right]^{-\\;2}$ is 729.<\/p>\n\n\n\n<p><strong>3. Find: <\/strong>$\\left[(125)^{6}\\right]^{\\frac{1}{2}}$<strong>.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Formula: $(x^{m})^{\\frac{p}{q}} = x^{\\frac{pm}{q}}$<\/p>\n\n\n\n<p>$\\left[(125)^{6}\\right]^{\\frac{1}{2}}$<\/p>\n\n\n\n<p>$= (125)^{6 \u00d7 \\frac{1}{2}}$<\/p>\n\n\n\n<p>$= (125)^{3}$<\/p>\n\n\n\n<p>$= 5$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-practice-problems-on-the-power-of-a-power-rule\">Practice Problems on the Power of a Power Rule<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Power of a Power Rule: Definition, Rules, Examples, Facts, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Find the correct answer for the following: $(a^{-\\;m})^{-\\;n} =$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$a^{-\\;m + n}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$a^{-\\;mn}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$a^{mn}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$a^{\\frac{m}{n}}$<\/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: $a^{mn}$<br\/>Based on the power of a power rule for negative exponent formula,<br>\r\n$(a^{-\\;m})^{-\\;n} = a^{mn}$<\/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\">Calculate the value of $\\left[(\\;-\\;3)^{-\\;2}\\right]^{-\\;4}$.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$(\\;-\\;3)^{8}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$(\\;-\\;3)^{-\\;6}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\;-\\;(\\;-\\;3)^{8}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$(\\;-\\;3)^{-\\;8}$<\/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: $(\\;-\\;3)^{8}$<br\/>$\\left[(\\;-\\;3)^{-\\;2}\\right]^{-\\;4} = (\\;-\\;3)^{-\\;2 \u00d7 \\;-\\;4} = (\\;-\\;3)^{8}$<\/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\">Simplify the following: $\\;-\\;3 + (5^{2})^{\\frac{1}{2}}$.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">1<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\;-\\;2$<\/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: 2<br\/>$\\;-\\;3 + (5^{2})^{\\frac{1}{2}} = \\;-\\;3 + 5^{1} = 2$<\/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\": \"Power of a Power Rule: Definition, Rules, 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\"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$a^{-\\\\;m + n}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Based on the power of a power rule for negative exponent formula,<br>\r\n$$(a^{-\\\\;m})^{-\\\\;n} = a^{mn}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$a^{-\\\\;mn}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Based on the power of a power rule for negative exponent 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                         \"@type\": \"Comment\",\n                          \"text\": \"Based on the power of a power rule for negative exponent formula,<br>\r\n$$(a^{-\\\\;m})^{-\\\\;n} = a^{mn}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Based on the power of a power rule for negative exponent formula,<br>\r\n$$(a^{-\\\\;m})^{-\\\\;n} = a^{mn}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Calculate the value of $$\\\\left[(\\\\;-\\\\;3)^{-\\\\;2}\\\\right]^{-\\\\;4}$$.\",\n                    \"text\": \"Calculate the value of $$\\\\left[(\\\\;-\\\\;3)^{-\\\\;2}\\\\right]^{-\\\\;4}$$.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$\\\\left[(\\\\;-\\\\;3)^{-\\\\;2}\\\\right]^{-\\\\;4} = (\\\\;-\\\\;3)^{-\\\\;2 \u00d7 \\\\;-\\\\;4} = (\\\\;-\\\\;3)^{8}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(\\\\;-\\\\;3)^{-\\\\;6}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\left[(\\\\;-\\\\;3)^{-\\\\;2}\\\\right]^{-\\\\;4} = (\\\\;-\\\\;3)^{-\\\\;2 \u00d7 \\\\;-\\\\;4} = (\\\\;-\\\\;3)^{8}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\;-\\\\;(\\\\;-\\\\;3)^{8}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\left[(\\\\;-\\\\;3)^{-\\\\;2}\\\\right]^{-\\\\;4} = (\\\\;-\\\\;3)^{-\\\\;2 \u00d7 \\\\;-\\\\;4} = (\\\\;-\\\\;3)^{8}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(\\\\;-\\\\;3)^{-\\\\;8}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\left[(\\\\;-\\\\;3)^{-\\\\;2}\\\\right]^{-\\\\;4} = (\\\\;-\\\\;3)^{-\\\\;2 \u00d7 \\\\;-\\\\;4} = (\\\\;-\\\\;3)^{8}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$(\\\\;-\\\\;3)^{8}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$\\\\left[(\\\\;-\\\\;3)^{-\\\\;2}\\\\right]^{-\\\\;4} = (\\\\;-\\\\;3)^{-\\\\;2 \u00d7 \\\\;-\\\\;4} = (\\\\;-\\\\;3)^{8}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$\\\\left[(\\\\;-\\\\;3)^{-\\\\;2}\\\\right]^{-\\\\;4} = (\\\\;-\\\\;3)^{-\\\\;2 \u00d7 \\\\;-\\\\;4} = (\\\\;-\\\\;3)^{8}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Simplify the following: $$\\\\;-\\\\;3 + (5^{2})^{\\\\frac{1}{2}}$$.\",\n                    \"text\": \"Simplify the following: $$\\\\;-\\\\;3 + (5^{2})^{\\\\frac{1}{2}}$$.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$\\\\;-\\\\;3 + (5^{2})^{\\\\frac{1}{2}} = \\\\;-\\\\;3 + 5^{1} = 2$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\;-\\\\;3 + (5^{2})^{\\\\frac{1}{2}} = \\\\;-\\\\;3 + 5^{1} = 2$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\;-\\\\;2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\;-\\\\;3 + (5^{2})^{\\\\frac{1}{2}} = \\\\;-\\\\;3 + 5^{1} = 2$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\;-\\\\;1$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\;-\\\\;3 + (5^{2})^{\\\\frac{1}{2}} = \\\\;-\\\\;3 + 5^{1} = 2$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"2\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$\\\\;-\\\\;3 + (5^{2})^{\\\\frac{1}{2}} = \\\\;-\\\\;3 + 5^{1} = 2$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$\\\\;-\\\\;3 + (5^{2})^{\\\\frac{1}{2}} = \\\\;-\\\\;3 + 5^{1} = 2$$\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-frequently-asked-questions-on-the-power-of-a-power-rule\">Frequently Asked Questions on the Power of a Power Rule<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-b70d649b-b3d5-4970-9c47-1d7ae42928cf\" 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-b70d649b-b3d5-4970-9c47-1d7ae42928cf\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b70d649b-b3d5-4970-9c47-1d7ae42928cf\"><strong>What is the fraction power to power rule?<\/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-b70d649b-b3d5-4970-9c47-1d7ae42928cf\">\n\n<p>$(x^{\\frac{m}{n}})^{\\frac{p}{q}} = x^{\\frac{pm}{nq}}$<\/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-b70d649b-b3d5-4970-9c47-1d7ae42928cf\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b70d649b-b3d5-4970-9c47-1d7ae42928cf\"><strong>How to apply the power to the power 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-b70d649b-b3d5-4970-9c47-1d7ae42928cf\">\n\n<p>If the base a is raised to a power m and the entire expression $a^{m}$ is again raised to the power n, then we keep the same base and multiply the powers\u00a0 $(a^{m})^{n} = a^{mn}$.<\/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-b70d649b-b3d5-4970-9c47-1d7ae42928cf\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b70d649b-b3d5-4970-9c47-1d7ae42928cf\"><strong>What is the product rule of 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-b70d649b-b3d5-4970-9c47-1d7ae42928cf\">\n\n<p>$a^{m} \\times a^{n} = a^{m\\timesn}$<\/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-b70d649b-b3d5-4970-9c47-1d7ae42928cf\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b70d649b-b3d5-4970-9c47-1d7ae42928cf\"><strong>What is the negative exponent rule and the power of a power rule in algebra?<\/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-b70d649b-b3d5-4970-9c47-1d7ae42928cf\">\n\n<p>Power of a power rule:<strong> <\/strong>$(a^{m})^{n} = a^{mn}$<\/p>\n\n\n\n<p>Negative Exponent Rule: $a^{-m} = \\frac{1}{a^{m}}$<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Power of a Power Rule? The power of a power rule is an important exponent rule (law of exponent) used to simplify an expression of the form $(x^{m})^{n}$, where the base x is raised to a power m and the entire expression $x^{m}$ is raised to the power n again.\u00a0 Power raised &#8230; <a title=\"Power of a Power Rule: Definition, Rules, Examples, Facts, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/power-of-a-power-rule\" aria-label=\"More on Power of a Power Rule: Definition, Rules, Examples, Facts, 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-32643","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\/32643","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=32643"}],"version-history":[{"count":11,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/32643\/revisions"}],"predecessor-version":[{"id":32668,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/32643\/revisions\/32668"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=32643"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=32643"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=32643"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}