{"id":114,"date":"2022-04-12T12:08:52","date_gmt":"2022-04-12T12:08:52","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=114"},"modified":"2025-10-14T09:04:11","modified_gmt":"2025-10-14T09:04:11","slug":"f-13-identify-equivalent-expressions-involving-exponents","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/f-13-identify-equivalent-expressions-involving-exponents\/","title":{"rendered":"F.13 Identify equivalent expressions involving exponents"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-huge-font-size\" style=\"color:#00056d;text-transform:uppercase\"><strong>Identify equivalent expressions involving exponents<\/strong><\/h2>\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-7eac2941a6ce85b5d1bae8eb7923d812\">\ud83c\udf1f<strong> Identify Equivalent Expressions Involving 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>\ud83d\udd39<strong> What are Equivalent Exponential Expressions?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\ud83d\udc49 Two expressions are <strong>equivalent<\/strong> if they have the <strong>same value<\/strong>, even if they look different.<\/p>\n\n\n\n<p><strong>\u2705 Example:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2<sup>3<\/sup>\u00d72<sup>2<\/sup>=2<sup>3+2<\/sup>=2<sup>5<\/sup><\/li>\n\n\n\n<li>So, 2<sup>3<\/sup>\u00d72<sup>2<\/sup> and 2<sup>5<\/sup> are <strong>equivalent expressions<\/strong>.<\/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>\ud83d\udd39 <strong>Basic Exponent Rules (Laws of Exponents)<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>These rules help us find and simplify equivalent exponential expressions:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th><strong>Rule Name<\/strong><\/th><th><strong>Formula<\/strong><\/th><th><strong>Example<\/strong><\/th><\/tr><\/thead><tbody><tr><td><strong>Product Rule<\/strong><\/td><td>a<sup>m<\/sup>\u00d7a<sup>n<\/sup>=a<sup>m+n<\/sup><\/td><td>3<sup>2<\/sup>\u00d73<sup>4<\/sup>=3<sup>6<\/sup><\/td><\/tr><tr><td><strong>Quotient Rule<\/strong><\/td><td>a<sup>m<\/sup>\/a<sup>n<\/sup>=a<sup>m\u2212n<\/sup><\/td><td>5<sup>6<\/sup>\/5<sup>2<\/sup>=5<sup>4<\/sup><\/td><\/tr><tr><td><strong>Power Rule<\/strong><\/td><td>(a<sup>m<\/sup>)<sup>n<\/sup>=a<sup>m\u00d7n<\/sup><\/td><td>(2<sup>3<\/sup>)<sup>2<\/sup>=2<sup>6<\/sup><\/td><\/tr><tr><td><strong>Zero Exponent Rule<\/strong><\/td><td>a<sup>0<\/sup>=1(where a\u22600)<\/td><td>7<sup>0<\/sup>=1<\/td><\/tr><tr><td><strong>Negative Exponent Rule<\/strong><\/td><td>a<sup>\u2212n<\/sup>=1\/a<sup>n<\/sup><\/td><td>4<sup>\u22122<\/sup>=1\/4<sup>2<\/sup>=1\/16<\/td><\/tr><tr><td><strong>Power of a Product<\/strong><\/td><td>(ab)<sup>m<\/sup>=a<sup>m<\/sup>\u00d7b<sup>m<\/sup><\/td><td>(2\u00d73)<sup>2<\/sup>=2<sup>2<\/sup>\u00d73<sup>2<\/sup><\/td><\/tr><tr><td><strong>Power of a Quotient<\/strong><\/td><td>(a\/b)<sup>m<\/sup>=a<sup>m<\/sup>\/b<sup>m<\/sup><\/td><td>(2\/5)<sup>3<\/sup>=2<sup>3<\/sup>\/5<sup>3<\/sup><\/td><\/tr><\/tbody><\/table><\/figure>\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>How to Identify Equivalent Expressions<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\ud83d\udc49 To check if two exponential expressions are <strong>equivalent<\/strong>, use these steps:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Simplify<\/strong> both expressions using exponent rules.<\/li>\n\n\n\n<li><strong>Compare<\/strong> the base and the exponent.<\/li>\n\n\n\n<li>If both are the same after simplification \u2192 \u2705 <strong>Equivalent!<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>\ud83e\uddee Example:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Check if (x<sup>2<\/sup>)<sup>3<\/sup> and x<sup>6<\/sup> are equivalent.<\/li>\n\n\n\n<li>Simplify: (x<sup>2<\/sup>)<sup>3<\/sup>=x<sup>2\u00d73<\/sup>=x<sup>6<\/sup><\/li>\n\n\n\n<li>\u2705 Both are equivalent.<\/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>\ud83d\udd39 <strong>Common Mistakes to Avoid \u274c<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u26a0\ufe0f Don\u2019t add or multiply exponents when bases are different.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Example: 2<sup>3<\/sup>+3<sup>3<\/sup>\u22605<sup>3<\/sup> \u274c<\/li>\n<\/ul>\n\n\n\n<p>\u26a0\ufe0f Remember that (a+b)<sup>n<\/sup>\u2260a<sup>n<\/sup>+b<sup>n<\/sup><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Example: (2+3)<sup>2<\/sup>=25, but 2<sup>2<\/sup>+3<sup>2<\/sup>=13 \u2014 not equal!<\/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>\ud83d\udd39 <strong>Real-Life Connection \ud83c\udf0d<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Exponents are used to express:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Area and volume formulas<\/strong> (e.g., s<sup>2<\/sup>, s<sup>3<\/sup>)<\/li>\n\n\n\n<li><strong>Scientific notation<\/strong> (3\u00d710<sup>5<\/sup>)<\/li>\n\n\n\n<li><strong>Growth patterns<\/strong> (population, bacteria growth, etc.)<\/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>\u2728 <strong>Summary<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Equivalent expressions have the <strong>same value<\/strong>.<\/li>\n\n\n\n<li>Use <strong>exponent rules<\/strong> to simplify expressions.<\/li>\n\n\n\n<li>Always <strong>check bases and exponents<\/strong>.<\/li>\n\n\n\n<li>Avoid common exponent errors.<\/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 Practice<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Are 2<sup>3<\/sup>\u00d72<sup>4<\/sup> and 2<sup>7<\/sup> equivalent? \u2705<\/li>\n\n\n\n<li>Is (x<sup>2<\/sup>)<sup>3<\/sup>=x<sup>6<\/sup>? \u2705<\/li>\n\n\n\n<li>Is 3<sup>4<\/sup>\u00f73<sup>2<\/sup>=3<sup>2<\/sup>? \u2705<\/li>\n\n\n\n<li>Is (2\u00d73)<sup>2<\/sup>=2<sup>2<\/sup>+3<sup>2<\/sup>? \u274c<\/li>\n<\/ol>\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 has-background has-normal-font-size\" style=\"background-color:#b6f3d8\"><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-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-824d9fa0cde8ddbe52a7bb87a2f60f53\" style=\"color:#b00012\"><strong>Select&nbsp;all the expressions that are equivalent to&nbsp;8<sup>5<\/sup>,3<sup>-3<\/sup><\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1\/8<sup>-9<\/sup><\/li>\n\n\n\n<li>8<sup>-9<\/sup><\/li>\n\n\n\n<li>8<\/li>\n\n\n\n<li>8<sup>0<\/sup><\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>To find which expressions are equivalent to 8<sup>3<\/sup>.8<sup>-3<\/sup>, write each expression with the same base.<\/p>\n\n\n\n<p>The answer choices and 8<sup>3<\/sup> . 8 <sup>\u20133<\/sup> can all be written as a power of 8. So, use properties of exponents to write each expression in the form 8 <sup>( )<\/sup>. Then, see which ones match 8<sup>3<\/sup> . 8 <sup>\u20133<\/sup>  in this form.<\/p>\n\n\n\n<p>Step 1: Write 8<sup>3<\/sup>.8<sup>\u20133<\/sup> in the form 8<sup>( )<\/sup><\/p>\n\n\n\n<p>8<sup>3<\/sup>.8<sup>\u20133<\/sup><\/p>\n\n\n\n<p>= 8<sup>3+-3<\/sup>           Use the identity a<sup>x<\/sup>a<sup>y<\/sup> = a<sup>x+y<\/sup><\/p>\n\n\n\n<p>= 8<sup>0<\/sup>            <\/p>\n\n\n\n<p>A positive number raised to zeroth power is 1. So, 8<sup>3<\/sup> . 8-<sup>3<\/sup> &nbsp;is equal to&nbsp;1.<\/p>\n\n\n\n<p>Step 2: Now see which expressions are also equal to 8<sup>0<\/sup> = 1.<\/p>\n\n\n\n<p>See if 1 \/ 8<sup>-9<\/sup> is equal to 1.<\/p>\n\n\n\n<p>1 \/ 8<sup>-9<\/sup><\/p>\n\n\n\n<p>=8<sup>-(-9)<\/sup>     Use the identity  1\/a<sup>x<\/sup>=a<sup>\u2013x<\/sup><\/p>\n\n\n\n<p>= 8<sup>9<\/sup><\/p>\n\n\n\n<p>So, 1 \/ 8<sup>-9<\/sup> is equal to 8<sup>9<\/sup>, but 8<sup>3<\/sup> . 8-<sup>3<\/sup> is not. (It is equal to 8<sup>0<\/sup>=1.)<br>The expressions1 \/ 8<sup>-9<\/sup>and 8<sup>3<\/sup> . 8-<sup>3<\/sup>are not equivalent.<\/p>\n\n\n\n<p>The&nbsp;expression 8<sup>-9<\/sup> is in the form 8 . You&#8217;ve already found that 8<sup>3<\/sup> . 8-<sup>3<\/sup> is not equal to 8<sup>-9<\/sup> (It is equal to 8<sup>0<\/sup>=1)<\/p>\n\n\n\n<p>The&nbsp;expression 8<sup>-9<\/sup> and&nbsp; 8<sup>3<\/sup> . 8-<sup>3<\/sup> are not equivalent.<\/p>\n\n\n\n<p>8 is not equal to 1 , but  8<sup>3<\/sup> . 8-<sup>3<\/sup> is equal to 1<\/p>\n\n\n\n<p>The expression 8 and 8<sup>3<\/sup> . 8-<sup>3<\/sup> are not equivalent.<\/p>\n\n\n\n<p>you&#8217;ve already found 8<sup>3<\/sup> . 8-<sup>3<\/sup> is equal to 8<sup>0<\/sup> .<\/p>\n\n\n\n<p>The expression 8<sup>0<\/sup> and&nbsp; 8<sup>3<\/sup> . 8-<sup>3<\/sup> are equivalent.<\/p>\n\n\n\n<p>The correct answer is 8<sup>0<\/sup>.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#e68e8e\"><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-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-34ee82f6593f7617375c5eb5cfaed9a9\" style=\"color:#b00012\"><strong>Select all the expressions that are equivalent to (10<sup>3<\/sup>)<sup>0<\/sup>.<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>10<\/li>\n\n\n\n<li>1\/10<sup>0<\/sup><\/li>\n\n\n\n<li>1<\/li>\n\n\n\n<li>1\/10<sup>3<\/sup><\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>To find which expressions are equivalent to (10<sup>3<\/sup>)<sup>0<\/sup>, write each expression with the same base. <\/p>\n\n\n\n<p>The answer choices and (10<sup>3<\/sup>)<sup>0<\/sup> can all be written as a power of 10. So, use properties of exponents to write each expression in the form 10 <sup>( )<\/sup><br>. Then, see which ones match (10<sup>3<\/sup>)<sup>0<\/sup> in this form.<\/p>\n\n\n\n<p><strong>Step 1: Write (10<sup>3<\/sup>)<sup>0<\/sup> in the form 10.<\/strong><\/p>\n\n\n\n<p>(10<sup>3<\/sup>)<sup>0<\/sup><\/p>\n\n\n\n<p>= 10<sup>3.0<\/sup>          Use the identity (a<sup>x<\/sup>)<sup>y<\/sup>=a<sup>xy<\/sup><\/p>\n\n\n\n<p>=10<sup>0<\/sup><\/p>\n\n\n\n<p>A positive number raised to zero power is 1. So, (10<sup>3<\/sup>)<sup>0<\/sup> is equal to 1.<\/p>\n\n\n\n<p><strong>Step 2: Now see which expressions are also equal to 10<sup>0<\/sup>=1.<\/strong><\/p>\n\n\n\n<p>10 is not equal to 1, but (10<sup>3<\/sup>)<sup>0<\/sup> is equal to 1.<\/p>\n\n\n\n<p>The expressions 10 and (10<sup>3<\/sup>)<sup>0<\/sup> are not equivalent.<\/p>\n\n\n\n<p>See if 1\/10<sup>0<\/sup> is equal to 1.<\/p>\n\n\n\n<p>1\/10<sup>0<\/sup><\/p>\n\n\n\n<p>1\/1            Use the identity a0=1<\/p>\n\n\n\n<p>1<\/p>\n\n\n\n<p>Both 1\/10<sup>0<\/sup> and (10<sup>3<\/sup>)<sup>0 <\/sup>are equal to 1.<\/p>\n\n\n\n<p>The expressions 1\/10<sup>0<\/sup> and (10<sup>3<\/sup>)<sup>0<\/sup> are <strong>equivalent<\/strong>.<\/p>\n\n\n\n<p>You&#8217;ve already found that (10<sup>3<\/sup>)<sup>0<\/sup> is equal to 1.<br>The expressions 1 and (10<sup>3<\/sup>)<sup>0<\/sup> are equivalent.<\/p>\n\n\n\n<p>See if 1\/10<sup>3<\/sup> is equal to 1.<\/p>\n\n\n\n<p>1\/10<sup>3<\/sup><\/p>\n\n\n\n<p>=10<sup>\u20133<\/sup>                  <\/p>\n\n\n\n<p>Use the identity<br>1\/a<sup>x<\/sup>=a<sup>\u2013x<\/sup><\/p>\n\n\n\n<p>So, 1\/10<sup>3<\/sup> is equal to 10<sup>\u20133<\/sup>, but (10<sup>3<\/sup>)<sup>0<\/sup> is not. (It is equal to 10<sup>0<\/sup>=1.)<br>The expressions 1\/10<sup>3<\/sup> and (10<sup>3<\/sup>)<sup>0<\/sup> are not equivalent.<\/p>\n\n\n\n<p>The correct answers are:<\/p>\n\n\n\n<p>=1\/10<sup>0<\/sup><\/p>\n\n\n\n<p>=1<\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s practice!<\/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\/78201\/531\/145\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-299.png\" alt=\"\" class=\"wp-image-9590\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-299.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-299-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-299-150x150.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\/33894\/202\/781\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-306.png\" alt=\"\" class=\"wp-image-9592\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-306.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-306-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-306-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Identify equivalent expressions involving exponents Key Notes : \ud83c\udf1f Identify Equivalent Expressions Involving Exponents \ud83d\udd39 What are Equivalent Exponential Expressions? \ud83d\udc49 Two expressions are equivalent if they have the same value, even if they look different. \u2705 Example: \ud83d\udd39 Basic Exponent Rules (Laws of Exponents) These rules help us find and simplify equivalent exponential expressions:<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/f-13-identify-equivalent-expressions-involving-exponents\/\">Continue reading <span class=\"screen-reader-text\">&#8220;F.13 Identify equivalent expressions involving 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-114","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\/114","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=114"}],"version-history":[{"count":21,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/114\/revisions"}],"predecessor-version":[{"id":21872,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/114\/revisions\/21872"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=114"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}