{"id":110,"date":"2022-04-12T12:08:14","date_gmt":"2022-04-12T12:08:14","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=110"},"modified":"2025-10-29T09:36:24","modified_gmt":"2025-10-29T09:36:24","slug":"f-11-power-rule","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/f-11-power-rule\/","title":{"rendered":"F.11 Power rule"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-link-color wp-elements-8639deaed4cec90e4b0ec0c167504b65\" style=\"color:#00056d;text-transform:uppercase\"><strong>Power rule<\/strong><\/h2>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div style=\"position: relative; width: 100%; height: 0; padding-top: 56.2500%;\n padding-bottom: 0; box-shadow: 0 2px 8px 0 rgba(63,69,81,0.16); margin-top: 1.6em; margin-bottom: 0.9em; overflow: hidden;\n border-radius: 8px; will-change: transform;\">\n  <iframe loading=\"lazy\" style=\"position: absolute; width: 100%; height: 100%; top: 0; left: 0; border: none; padding: 0;margin: 0;\"\n    src=\"https:\/\/www.canva.com\/design\/DAG3KXqOsms\/1W7ODKEG_MQzTAphIM6D7w\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAG3KXqOsms&#x2F;1W7ODKEG_MQzTAphIM6D7w&#x2F;watch?utm_content=DAG3KXqOsms&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">Design<\/a> by Delta publications\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-09eb8d27d0d70f35bd20b1cf47293f11\" style=\"color:#74008b\"><strong>Key Notes :<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading has-primary-color has-text-color has-link-color has-large-font-size wp-elements-22a537406f94bb5ba8c947f10e59965d\">\ud83e\uddee <strong>Power Rule<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td>\ud83d\udd39 <strong>What is the Power Rule?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>The <strong>Power Rule<\/strong> is a rule used to simplify and solve problems involving <strong>exponents<\/strong> (also called powers).<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td>\ud83d\udcd8 <strong>Basic Power Rules<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>1. Product of Powers Rule<\/strong> <\/p>\n\n\n\n<p class=\"has-text-align-center\">a<sup>m<\/sup>\u00d7a<sup>n<\/sup>=a<sup>m+n<\/sup><\/p>\n\n\n\n<p> \u27a4 When you <strong>multiply powers with the same base<\/strong>, <strong>add the exponents<\/strong>.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Example:<\/strong> 3<sup>2<\/sup>\u00d73<sup>4<\/sup>=3<sup>2+4<\/sup>=3<sup>6<\/sup><\/li>\n<\/ul>\n\n\n\n<p><strong>2. Quotient of Powers Rule<\/strong> <\/p>\n\n\n\n<p class=\"has-text-align-center\">a<sup>m<\/sup>\/a<sup>n<\/sup>=a<sup>m\u2212n<\/sup><\/p>\n\n\n\n<p>\u27a4 When you <strong>divide powers with the same base<\/strong>, <strong>subtract the exponents<\/strong>.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Example:<\/strong> 5<sup>6<\/sup>\u00f75<sup>2<\/sup>=5<sup>6\u22122<\/sup>=5<sup>4<\/sup><\/li>\n<\/ul>\n\n\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li><\/li>\n<\/ol>\n\n\n\n<p><strong>3. Power of a Power Rule<\/strong> <\/p>\n\n\n\n<p class=\"has-text-align-center\">(a<sup>m<\/sup>)<sup>n<\/sup>=a<sup>m\u00d7n<\/sup><\/p>\n\n\n\n<p> \u27a4 When you have a <strong>power raised to another power<\/strong>, <strong>multiply the exponents<\/strong>.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Example:<\/strong> (2<sup>3<\/sup>)<sup>2<\/sup>=2<sup>3\u00d72<\/sup>=2<sup>6<\/sup><\/li>\n<\/ul>\n\n\n\n<ol start=\"3\" class=\"wp-block-list\">\n<li><\/li>\n<\/ol>\n\n\n\n<p><strong>4. Power of a Product Rule<\/strong> <\/p>\n\n\n\n<p class=\"has-text-align-center\">(ab)<sup>n<\/sup>=a<sup>n<\/sup>\u00d7b<sup>n<\/sup><\/p>\n\n\n\n<p>\u27a4 When a <strong>product<\/strong> is raised to a power, <strong>apply the power to each factor<\/strong>.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Example:<\/strong> (2\u00d73)<sup>4<\/sup>=2<sup>4<\/sup>\u00d73<sup>4<\/sup><\/li>\n<\/ul>\n\n\n\n<ol start=\"4\" class=\"wp-block-list\">\n<li><\/li>\n<\/ol>\n\n\n\n<p><strong>5. Power of a Quotient Rule<\/strong> <\/p>\n\n\n\n<p class=\"has-text-align-center\">(a\/b)<sup>n<\/sup>=a<sup>n<\/sup>\/b<sup>n<\/sup><\/p>\n\n\n\n<p> \u27a4 When a <strong>fraction<\/strong> is raised to a power, <strong>apply the power to both numerator and denominator<\/strong>.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Example:<\/strong> (2\/3)<sup>3<\/sup>=2<sup>3<\/sup>\/3<sup>3<\/sup>=8\/27<\/li>\n<\/ul>\n\n\n\n<ol start=\"5\" class=\"wp-block-list\">\n<li><\/li>\n<\/ol>\n\n\n\n<p><strong>6. Zero Exponent Rule<\/strong> <\/p>\n\n\n\n<p class=\"has-text-align-center\">a<sup>0<\/sup>=1(a\u22600)<\/p>\n\n\n\n<p>\u27a4 Any <strong>non-zero number<\/strong> raised to the power of <strong>zero<\/strong> equals <strong>1<\/strong>.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Example:<\/strong> 9<sup>0<\/sup>=1<\/li>\n<\/ul>\n\n\n\n<ol start=\"6\" class=\"wp-block-list\">\n<li><\/li>\n<\/ol>\n\n\n\n<p><strong>7. Negative Exponent Rule<\/strong> <\/p>\n\n\n\n<p class=\"has-text-align-center\">a<sup>\u2212n<\/sup>=1\/a<sup>n<\/sup><\/p>\n\n\n\n<p>\u200b\u27a4 A <strong>negative exponent<\/strong> means take the <strong>reciprocal<\/strong> of the base.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Example:<\/strong> 2<sup>\u22123<\/sup>=1\/2<sup>3<\/sup>=1\/8<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td>\u26a1 <strong>Important Points to Remember<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The base must be the <strong>same<\/strong> to apply most rules.<\/li>\n\n\n\n<li>Exponents show <strong>repeated multiplication<\/strong>.<\/li>\n\n\n\n<li>Always <strong>simplify step-by-step<\/strong> using these rules.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td>\ud83e\udde0 <strong>Example Problems<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li>(x<sup>3<\/sup>)<sup>4<\/sup>=x<sup>3\u00d74<\/sup>=x<sup>12<\/sup><\/li>\n\n\n\n<li>a<sup>5<\/sup>\u00d7a<sup>2<\/sup>=a<sup>5+2<\/sup>=a<sup>7<\/sup><\/li>\n\n\n\n<li>y<sup>8<\/sup>\/y<sup>3<\/sup>=y<sup>8\u22123<\/sup>=y<sup>5<\/sup><\/li>\n\n\n\n<li>(2x)<sup>3<\/sup>=2<sup>3<\/sup>.x<sup>3<\/sup>=8x<sup>3<\/sup><\/li>\n\n\n\n<li>(3<sup>2<\/sup>)<sup>0<\/sup>=1<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td>\ud83c\udfaf <strong>Summary Table<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Rule Name<\/th><th>Formula<\/th><th>Example<\/th><\/tr><\/thead><tbody><tr><td>Product of Powers<\/td><td>a<sup>m<\/sup>\u00d7a<sup>n<\/sup>=a<sup>m+n<\/sup><\/td><td>x<sup>2<\/sup>.x<sup>3<\/sup>=x<sup>5<\/sup><\/td><\/tr><tr><td>Quotient of Powers<\/td><td>a<sup>m<\/sup>\/a<sup>n<\/sup>=a<sup>m\u2212n<\/sup><\/td><td>y<sup>6<\/sup>\u00f7y<sup>2<\/sup>=y<sup>4<\/sup><\/td><\/tr><tr><td>Power of a Power<\/td><td>(a<sup>m<\/sup>)<sup>n<\/sup>=a<sup>mn<\/sup><\/td><td>(3<sup>2<\/sup>)<sup>3<\/sup>=3<sup>6<\/sup><\/td><\/tr><tr><td>Power of a Product<\/td><td>(ab)<sup>n<\/sup>=a<sup>n<\/sup>b<sup>n<\/sup><\/td><td>(2x)<sup>3<\/sup>=8x<sup>3<\/sup><\/td><\/tr><tr><td>Power of a Quotient<\/td><td>(a\/b)<sup>n<\/sup>=a<sup>n<\/sup>\/b<sup>n<\/sup>\u200b<\/td><td>(x\/2)<sup>2<\/sup>=x<sup>2<\/sup>\/4<\/td><\/tr><tr><td>Zero Exponent<\/td><td>a<sup>0<\/sup>=1<\/td><td>5<sup>0<\/sup>=1<\/td><\/tr><tr><td>Negative Exponent<\/td><td>a<sup>\u2212n<\/sup>=1\/a<sup>n<\/sup><\/td><td>4<sup>\u22122<\/sup>=1\/16<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-normal-font-size wp-elements-6b47067c76d81c865ae849c673396daa\" style=\"background-color:#92f2f7\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-text-color has-background has-link-color wp-elements-d1e96250eefc3d9d699eef9a22455655\" style=\"color:#b00012\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p><strong>Simplify.&nbsp;Express your answer using a single&nbsp;exponent.<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-foreground-color has-text-color has-link-color wp-elements-ea84893f00800e1c6c164ad85049acf3\">(v<sup>6<\/sup>)<sup>8<\/sup><\/p>\n<\/div><\/div>\n\n\n\n<p>The&nbsp;expression&nbsp;v<sup>6<\/sup>&nbsp;is raised to the power of&nbsp;8.&nbsp;Multiply the&nbsp;exponents.<\/p>\n\n\n\n<p class=\"has-text-align-center\">(v<sup>6<\/sup>)<sup>8 <\/sup>= v<sup>6.8<\/sup> &#8212;-&gt;<em>Simplify&nbsp;<\/em>(v<sup>6<\/sup>)<sup>8<\/sup> ,<em>&nbsp;remembering to multiply the&nbsp;exponents<\/em><\/p>\n\n\n\n<p>=v<sup>48<\/sup> &#8212;-&gt;<em>Multiply<\/em><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-normal-font-size wp-elements-fd6d1de9d67e5815c5a7409265762bf3\" style=\"background-color:#94f39c\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-text-color has-background has-link-color wp-elements-ba33d880a500a16b6467d2202f680f9e\" style=\"color:#b00012\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p><strong>Simplify.&nbsp;Express your answer using a single&nbsp;exponent.<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-foreground-color has-text-color has-link-color wp-elements-915587c81cfb2fdf10f07b64e0541bd6\">(v<sup>6<\/sup>)<sup>5<\/sup><\/p>\n<\/div><\/div>\n\n\n\n<p>The&nbsp;expression&nbsp;v<sup>6<\/sup>&nbsp;is raised to the power of&nbsp;5.&nbsp;Multiply the&nbsp;exponents.<\/p>\n\n\n\n<p class=\"has-text-align-center\">(v<sup>6<\/sup>)<sup>5 <\/sup>= v<sup>6.5<\/sup> &#8212;-&gt;<em>Simplify&nbsp;<\/em>(v<sup>6<\/sup>)<sup>5<\/sup> ,<em>&nbsp;remembering to multiply the&nbsp;exponents<\/em><\/p>\n\n\n\n<p>=v<sup>30<\/sup> &#8212;-&gt;<em>Multiply<\/em><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-normal-font-size wp-elements-edfc377aa6e63d6d62deba98280e9328\" style=\"background-color:#f3a3c3\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-text-color has-background has-link-color wp-elements-aa9c8c559cc7de511b94f34debfb3b5d\" style=\"color:#b00012\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p><strong>Simplify.&nbsp;Express your answer using a single&nbsp;exponent.<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-foreground-color has-text-color has-link-color wp-elements-c0bea8b9e9fadfd65411939ce8a1d4f2\">(v<sup>2<\/sup>)<sup>5<\/sup><\/p>\n<\/div><\/div>\n\n\n\n<p>The&nbsp;expression&nbsp;v<sup>2<\/sup>&nbsp;is raised to the power of&nbsp;5.&nbsp;Multiply the&nbsp;exponents.<\/p>\n\n\n\n<p class=\"has-text-align-center\">(v<sup>2<\/sup>)<sup>5 <\/sup>= v<sup>2.5<\/sup> &#8212;-&gt;<em>Simplify&nbsp;<\/em>(v<sup>2<\/sup>)<sup>5<\/sup> ,<em>&nbsp;remembering to multiply the&nbsp;exponents<\/em><\/p>\n\n\n\n<p>=v<sup>10<\/sup> &#8212;-&gt;<em>Multiply<\/em><\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\"><strong>Let&#8217;s practice!\ud83d\udd8a\ufe0f<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/78191\/662\/429\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-301.png\" alt=\"\" class=\"wp-image-9600\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-301.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-301-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-301-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/33893\/394\/337\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-308.png\" alt=\"\" class=\"wp-image-9601\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-308.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-308-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-308-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Power rule Design by Delta publications Key Notes : \ud83e\uddee Power Rule \ud83d\udd39 What is the Power Rule? The Power Rule is a rule used to simplify and solve problems involving exponents (also called powers). \ud83d\udcd8 Basic Power Rules 1. Product of Powers Rule am\u00d7an=am+n \u27a4 When you multiply powers with the same base, add<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/f-11-power-rule\/\">Continue reading <span class=\"screen-reader-text\">&#8220;F.11 Power rule&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-110","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_hostinger_reach_plugin_has_subscription_block":false,"_hostinger_reach_plugin_is_elementor":false,"_links":{"self":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/110","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=110"}],"version-history":[{"count":23,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/110\/revisions"}],"predecessor-version":[{"id":22053,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/110\/revisions\/22053"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=110"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}