{"id":112,"date":"2022-04-12T12:08:33","date_gmt":"2022-04-12T12:08:33","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=112"},"modified":"2025-10-29T09:40:42","modified_gmt":"2025-10-29T09:40:42","slug":"f-12-evaluate-expressions-using-properties-of-exponents","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/f-12-evaluate-expressions-using-properties-of-exponents\/","title":{"rendered":"F.12 Evaluate expressions using properties of exponents"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-link-color has-huge-font-size wp-elements-95a7ab0e7ced1e1e1b37b9e58cac567f\" style=\"color:#00056d;text-transform:uppercase\"><strong>Evaluate expressions using properties of exponents<\/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\/DAG3KTjrWIE\/mMpk-jzhyBdWKDGlhJCHzQ\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAG3KTjrWIE&#x2F;mMpk-jzhyBdWKDGlhJCHzQ&#x2F;watch?utm_content=DAG3KTjrWIE&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-0b48ffde0617fb128bc631699a39ade7\"><strong>\ud83c\udf1f Evaluate Expressions Using Properties of Exponents<\/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><strong>What is an Exponent?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\ud83d\udc49 An <strong>exponent<\/strong> tells how many times a number (called the <strong>base<\/strong>) is multiplied by itself.<\/p>\n\n\n\n<p><strong>Example:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2<sup>4<\/sup>=2\u00d72\u00d72\u00d72=16<\/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><strong>\u2699\ufe0f <strong>Basic Terms<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Base:<\/strong> The number that is multiplied.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\ud83d\udc49 In 5<sup>3<\/sup>, base = 5<\/li>\n<\/ul>\n\n\n\n<p><strong>Exponent (Power):<\/strong> The number of times the base is used as a factor.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\ud83d\udc49 In 5<sup>3<\/sup>, exponent = 3<\/li>\n<\/ul>\n\n\n\n<p><strong>Expression:<\/strong> A mathematical phrase with numbers, variables, and exponents.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\ud83d\udc49 Example: 3x<sup>2<\/sup>.x<sup>3<\/sup><\/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><strong>\ud83d\udca1 <strong>Properties of Exponents<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading has-normal-font-size\"><strong>1\ufe0f\u20e3 Product of Powers Property<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>When multiplying with the same base, <strong>add the exponents<\/strong>.<\/li>\n\n\n\n<li>\ud83d\udc49 a<sup>m<\/sup>\u00d7a<sup>n<\/sup>=a<sup>m+n<\/sup><\/li>\n\n\n\n<li>\ud83d\udcd8 Example: 2<sup>3<\/sup>\u00d72<sup>4<\/sup>=2<sup>3+4<\/sup>=2<sup>7<\/sup>=128<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-normal-font-size\">2\ufe0f\u20e3 <strong>Quotient of Powers Property<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>When dividing with the same base, <strong>subtract the exponents<\/strong>.<\/li>\n\n\n\n<li>\ud83d\udc49 a<sup>m<\/sup>\u00f7a<sup>n<\/sup>=a<sup>m\u2212n<\/sup><\/li>\n\n\n\n<li>\ud83d\udcd8 Example: 5<sup>6<\/sup>\u00f75<sup>2<\/sup>=5<sup>6\u22122<\/sup>=5<sup>4<\/sup>=625<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-normal-font-size\">3\ufe0f\u20e3 <strong>Power of a Power Property<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>When a power is raised to another power, <strong>multiply the exponents<\/strong>.<\/li>\n\n\n\n<li>\ud83d\udc49 (a<sup>m<\/sup>)<sup>n<\/sup>=a<sup>m\u00d7n<\/sup><\/li>\n\n\n\n<li>\ud83d\udcd8 Example: (3<sup>2<\/sup>)<sup>4<\/sup>=3<sup>8<\/sup>=6561<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-normal-font-size\">4\ufe0f\u20e3 <strong>Power of a Product Property<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Distribute the exponent to <strong>each factor<\/strong> inside the parentheses.<\/li>\n\n\n\n<li>\ud83d\udc49 (ab)<sup>m<\/sup>=a<sup>m<\/sup>\u00d7b<sup>m<\/sup><\/li>\n\n\n\n<li>\ud83d\udcd8 Example: (2x)<sup>3<\/sup>=2<sup>3<\/sup>\u00d7x<sup>3<\/sup>=8&#215;3<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-normal-font-size\">5\ufe0f\u20e3 <strong>Power of a Quotient Property<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Apply the exponent to both numerator and denominator.<\/li>\n\n\n\n<li>\ud83d\udc49 (a\/b)<sup>m<\/sup>=a<sup>m<\/sup>\/b<sup>m<\/sup><\/li>\n\n\n\n<li>\ud83d\udcd8 Example: (3\/2)<sup>2<\/sup>=3<sup>2<\/sup>\/2<sup>2<\/sup>=9\/4<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-normal-font-size\">6\ufe0f\u20e3 <strong>Zero Exponent Rule<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Any nonzero number raised to the power of <strong>0<\/strong> is <strong>1<\/strong>.<\/li>\n\n\n\n<li>\ud83d\udc49 a<sup>0<\/sup>=1<\/li>\n\n\n\n<li>\ud83d\udcd8 Example: 9<sup>0<\/sup>=1<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-normal-font-size\">7\ufe0f\u20e3 <strong>Negative Exponent Rule<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A negative exponent means <strong>take the reciprocal<\/strong> of the base.<\/li>\n\n\n\n<li>\ud83d\udc49 a<sup>\u2212m<\/sup>=1\/a<sup>m<\/sup><\/li>\n\n\n\n<li>\ud83d\udcd8 Example: 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><strong>\ud83e\udde0 <strong>Steps to Evaluate Exponential Expressions<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>1\ufe0f\u20e3 Identify the <strong>base<\/strong> and <strong>exponent(s)<\/strong>.<\/p>\n\n\n\n<p>2\ufe0f\u20e3 Apply the <strong>rules of exponents<\/strong> (add, subtract, multiply).<\/p>\n\n\n\n<p>3\ufe0f\u20e3 Simplify <strong>numerical values<\/strong>.<\/p>\n\n\n\n<p>4\ufe0f\u20e3 If variables are present, simplify their powers using the same base rule.<\/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><strong>\ud83c\udfaf <strong>Example Problems<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li>3<sup>2<\/sup>\u00d73<sup>4<\/sup>=3<sup>6<\/sup>=729<\/li>\n\n\n\n<li>(x<sup>3<\/sup>)<sup>2<\/sup>=x<sup>6<\/sup><\/li>\n\n\n\n<li>y<sup>8<\/sup>\/y<sup>3<\/sup>=y<sup>5<\/sup><\/li>\n\n\n\n<li>(2a<sup>2<\/sup>b)<sup>3<\/sup>=2<sup>3<\/sup>a<sup>6<\/sup>b<sup>3<\/sup>=8a<sup>6<\/sup>b<sup>3<\/sup><\/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><strong>\ud83c\udf08 <strong>Key Tips<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u2728 Always check if the <strong>bases are the same<\/strong> before applying rules.<\/p>\n\n\n\n<p>\u2728 Simplify <strong>step by step<\/strong> to avoid mistakes.<\/p>\n\n\n\n<p>\u2728 Remember: These rules work only when <strong>bases are identical<\/strong>!<\/p>\n\n\n\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/h2>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-ed45ab2c8697fc6a47fee74a023c9fd5\" style=\"background-color:#f4ef88\"><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-795f748115f0dabb302d2cb0ced7e329\" style=\"color:#b00012\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p><strong>\ud83d\udd25Evaluate. Write your answer as a whole number or as a simplified fraction.<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\">12<sup>5<\/sup> \/12<sup>3<\/sup> =<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color\" style=\"color:#001690\">To divide powers with the same base, subtract their exponents.<\/p>\n\n\n\n<p>First, combine powers with the same bases.<\/p>\n\n\n\n<p class=\"has-text-align-center\">&nbsp;12<sup>5<\/sup> \/ 12<sup>3<\/sup>=&nbsp;<strong>12<sup><strong>5<\/strong>&nbsp;<strong>\u2212<\/strong>&nbsp;<strong>3<\/strong><\/sup><\/strong> &#8212;&#8211;&gt; Divide the 12&#8217;s, remembering to subtract the exponents<\/p>\n\n\n\n<p class=\"has-text-align-left\">&nbsp;                          =&nbsp;<strong>12<sup>2<\/sup><\/strong><\/p>\n\n\n\n<p>Now evaluate.<\/p>\n\n\n\n<p class=\"has-text-align-center\">12<sup>2<\/sup>&nbsp;= 144<\/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-large-font-size wp-elements-5b5276249f73e009cc93c5a3d6de1d60\" style=\"background-color:#c385f8\"><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-c1025a19f58938c3fce1680ff655f7be\" style=\"color:#b00012\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p><strong>\ud83d\udd25Evaluate. Write your answer as a whole number or as a simplified fraction.<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\">4<sup>2<\/sup>&nbsp;\u00b7&nbsp;4<sup>2<\/sup>&nbsp;=&nbsp;<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-primary-color has-text-color\">To multiply powers with the same base, keep the base and add the exponents.<\/p>\n\n\n\n<p>Evaluate.<\/p>\n\n\n\n<p>     4<sup>2<\/sup> \u00b7 4<sup>2<\/sup> = 16 \u00b7 4<sup>2<\/sup>              &#8212;&#8212;-&gt;Evaluate 4<sup>2<\/sup><\/p>\n\n\n\n<p>                 = 16 \u00b7 16              &#8212;&#8212;&#8212;-&gt;Evaluate 4<sup>2<\/sup><\/p>\n\n\n\n<p>                 = 256        &#8212;&#8212;&gt;Multiply<\/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-large-font-size wp-elements-10e59e1ffa73a2d8be87c097a9e39bd2\" style=\"background-color:#a7f7cf\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-text-color has-background has-link-color wp-elements-ebd520e4bd783f3430276a7c56be4401\" style=\"color:#b00012\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p><strong>\ud83d\udd25Evaluate. Write your answer as a whole number or as a simplified fraction.<\/strong><\/p>\n\n\n\n<p>                     2<sup>7<\/sup>\/2<sup>4<\/sup>=<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-f0f0032d694e81bfe34191d33eb2c5ab\">First combine powers with the same bases.<\/p>\n\n\n\n<p>2<sup>7<\/sup> \/ 2<sup>4<\/sup> = 2<sup>7-4<\/sup> &#8212;&#8211;&gt; Divide the 2&#8217;s, remembering to subtract the exponents<\/p>\n\n\n\n<p>             = 2<sup>3<\/sup><\/p>\n\n\n\n<p>Now evaluate.<\/p>\n\n\n\n<p>2<sup>3<\/sup> = 8<\/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!<\/strong><\/p>\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\/963\/306\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-300.png\" alt=\"\" class=\"wp-image-9594\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-300.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-300-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-300-150x150.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\/649\/869\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-307.png\" alt=\"\" class=\"wp-image-9595\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-307.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-307-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-307-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Evaluate expressions using properties of exponents Design by Delta publications Key Notes : \ud83c\udf1f Evaluate Expressions Using Properties of Exponents What is an Exponent? \ud83d\udc49 An exponent tells how many times a number (called the base) is multiplied by itself. Example: \u2699\ufe0f Basic Terms Base: The number that is multiplied. Exponent (Power): The number of<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/f-12-evaluate-expressions-using-properties-of-exponents\/\">Continue reading <span class=\"screen-reader-text\">&#8220;F.12 Evaluate expressions using properties of exponents&#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-112","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\/112","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=112"}],"version-history":[{"count":25,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/112\/revisions"}],"predecessor-version":[{"id":22054,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/112\/revisions\/22054"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=112"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}