{"id":357,"date":"2022-04-13T09:08:36","date_gmt":"2022-04-13T09:08:36","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=357"},"modified":"2024-10-23T14:41:45","modified_gmt":"2024-10-23T14:41:45","slug":"u-9-identify-equivalent-expressions-involving-exponents","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/u-9-identify-equivalent-expressions-involving-exponents\/","title":{"rendered":"U.9 Identify equivalent expressions involving exponents"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Identify equivalent expressions involving exponents<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#74008b\"><strong>Key Notes :<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p><strong>Understanding Equivalent Expressions<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Equivalent expressions are expressions that have the same value for all possible values of the variables involved.<\/li>\n\n\n\n<li>In the context of exponents, equivalent expressions are expressions that can be simplified to the same form using the properties of exponents.<\/li>\n<\/ul>\n\n\n\n<p><strong>Key Properties of Exponents<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Product Rule:<\/strong> a^m * a^n = a^(m+n)<\/li>\n\n\n\n<li><strong>Quotient Rule:<\/strong> a^m \/ a^n = a^(m-n)<\/li>\n\n\n\n<li><strong>Power Rule:<\/strong> (a^m)^n = a^(m*n)<\/li>\n\n\n\n<li><strong>Zero Exponent Rule:<\/strong> a^0 = 1 (where a \u2260 0)<\/li>\n\n\n\n<li><strong>Negative Exponent Rule:<\/strong> a^(-n) = 1\/a^n (where a \u2260 0)<\/li>\n<\/ul>\n\n\n\n<p><strong>Identifying Equivalent Expressions<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Apply the properties of exponents to simplify both expressions.<\/strong><\/li>\n\n\n\n<li><strong>Compare the simplified forms.<\/strong><\/li>\n\n\n\n<li><strong>If the simplified forms are identical, the expressions are equivalent.<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Examples:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Are 2\u00b3 * 2\u2074 and 2\u2077 equivalent?<\/strong>\n<ul class=\"wp-block-list\">\n<li>Simplify the first expression: 2^(3+4) = 2\u2077<\/li>\n\n\n\n<li>The simplified forms are identical, so the expressions are equivalent.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Are (3\u00b2)\u00b3 and 3\u2076 equivalent?<\/strong>\n<ul class=\"wp-block-list\">\n<li>Simplify the first expression: 3^(2*3) = 3\u2076<\/li>\n\n\n\n<li>The simplified forms are identical, so the expressions are equivalent.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div><\/div>\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-foreground-color has-text-color has-background has-large-font-size\" style=\"background-color:#f1d3d3\"><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\" style=\"color:#b00012\"><strong>Select all the expressions that are equivalent to 10<sup>3<\/sup> . 10<sup>-8<\/sup><\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1 \/ 10<sup>-24<\/sup><\/li>\n\n\n\n<li>10<sup>-5<\/sup><\/li>\n\n\n\n<li>1 \/ 10<sup>5<\/sup><\/li>\n\n\n\n<li>1 \/ 10<sup>-5<\/sup><\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>To&nbsp;find which expressions are equivalent to 10<sup>3<\/sup> .10<sup>-8 <\/sup> , write each expression with the same base.<\/p>\n\n\n\n<p>The answer choices and 10<sup>3<\/sup> .10<sup>-8<\/sup> can all be written as a power of 10. So, use properties of exponents to write each expression in the form 10 . Then, see which ones match 10<sup>3<\/sup> .10<sup>-8<\/sup> in this&nbsp;form.<\/p>\n\n\n\n<p><strong>Step&nbsp;1:<\/strong> <strong>Write<\/strong> 10<sup>3<\/sup> .10<sup>-8<\/sup> in the form 10<\/p>\n\n\n\n<p>10<sup>3<\/sup> .10<sup>-8<\/sup> <\/p>\n\n\n\n<p>10<sup>3+ -8 <\/sup>   Use the identity a<sup>x<\/sup> a<sup>y<\/sup> = a <sup>x+y<\/sup><\/p>\n\n\n\n<p>10<sup>-5<\/sup><\/p>\n\n\n\n<p>So,&nbsp;10<sup>3<\/sup> .10<sup>-8<\/sup> &nbsp;is equal to 10<sup>-5<\/sup>.<\/p>\n\n\n\n<p>Step 2: Now write each answer choice in the form 10 <\/p>\n\n\n\n<p>Write 1 \/ 10<sup>-24<\/sup> in the form&nbsp; 10 <\/p>\n\n\n\n<p>1 \/ 10<sup>-24<\/sup> <\/p>\n\n\n\n<p>10<sup>-(-24)<\/sup>    Use&nbsp;the identity 1\/a<sup>x <\/sup> = a<sup>-x<\/sup><\/p>\n\n\n\n<p>10<sup>24<\/sup><\/p>\n\n\n\n<p>So,1 \/ 10<sup>-24<\/sup>  is equal to 10<sup>24<\/sup> , but&nbsp;10<sup>3<\/sup> .10<sup>-8<\/sup> is not. (It is equal to 10<sup>-5<\/sup>)<\/p>\n\n\n\n<p>The&nbsp;expressions  1 \/ 10<sup>-24<\/sup>  and&nbsp;10<sup>3<\/sup> .10<sup>-8<\/sup> are not equivalent.<\/p>\n\n\n\n<p>The&nbsp;expression&nbsp; 10<sup>-5<\/sup> is in the form 10 . You&#8217;ve already found that 10<sup>3<\/sup> .10<sup>-8<\/sup> &nbsp;is equal to 10<sup>-5<\/sup><\/p>\n\n\n\n<p>The&nbsp;expressions&nbsp;10<sup>-5<\/sup> and&nbsp;10<sup>3<\/sup> .10<sup>-8<\/sup> are equivalent.<\/p>\n\n\n\n<p>Write&nbsp;1 \/ 10<sup>5<\/sup> in the form 10<\/p>\n\n\n\n<p>1 \/ 10<sup>5<\/sup><\/p>\n\n\n\n<p>=10<sup>-5 <\/sup> Use&nbsp;the identity 1 \/ a<sup>x <\/sup> = a<sup>-x<\/sup><\/p>\n\n\n\n<p>Both&nbsp;1 \/ 10<sup>5<\/sup> and&nbsp;10<sup>3<\/sup> .10<sup>-8<\/sup>  are equal to&nbsp;10<sup>-5 <\/sup><\/p>\n\n\n\n<p>The&nbsp;expressions 1 \/ 10<sup>5<\/sup> and&nbsp; 10<sup>3<\/sup> .10<sup>-8<\/sup> are equivalent.<\/p>\n\n\n\n<p>Write&nbsp; 1 \/ 10<sup>-5<\/sup> in the form 10<\/p>\n\n\n\n<p>1 \/ 10<sup>-5<\/sup><\/p>\n\n\n\n<p>= 10<sup>-(-5)<\/sup>   Use&nbsp;the identity 1 \/ a<sup>x <\/sup> = a<sup>-x<\/sup><\/p>\n\n\n\n<p>= 10<sup>5<\/sup><\/p>\n\n\n\n<p>So,&nbsp;1 \/ 10<sup>-5<\/sup> is equal to 10<sup>5<\/sup> ,&nbsp;but 10<sup>3<\/sup> .10<sup>-8<\/sup> is not. (It is equal to&nbsp;10<sup>-5<\/sup>)<\/p>\n\n\n\n<p>The&nbsp;expressions 1 \/ 10<sup>-5<\/sup>  and&nbsp; 10<sup>3<\/sup> .10<sup>-8<\/sup> are not equivalent.<\/p>\n\n\n\n<p>The&nbsp;correct answers&nbsp;are:<\/p>\n\n\n\n<ul class=\"wp-block-list\" id=\"yui_3_18_1_1_1704691712883_2685\">\n<li>10<sup>-5<\/sup> <\/li>\n\n\n\n<li>1 \/ 10<sup>5<\/sup><\/li>\n<\/ul>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#b2bce5\"><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\" style=\"color:#b00012\"><strong>Select all the expressions that are equivalent to 5<sup>7<\/sup> . 5<sup>-2<\/sup><\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1 \/ 5<sup>-5<\/sup><\/li>\n\n\n\n<li>1 \/ 5<sup>5<\/sup><\/li>\n\n\n\n<li>1 \/ 5<sup>-14<\/sup><\/li>\n\n\n\n<li>5<sup>-14<\/sup><\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>To&nbsp;find which expressions are equivalent to 5<sup>7<\/sup> . 5<sup>-2 <\/sup> , write each expression with the same base.<\/p>\n\n\n\n<p>The answer choices and 5<sup>7<\/sup> . 5<sup>-2<\/sup> can all be written as a power of 5. So, use properties of exponents to write each expression in the form 5 . Then, see which ones match 5<sup>7<\/sup> . 5<sup>-2<\/sup> in this&nbsp;form.<\/p>\n\n\n\n<p><strong>Step&nbsp;1:<\/strong> <strong>Write<\/strong> 5<sup>7<\/sup> . 5<sup>-2<\/sup> in the form 5<\/p>\n\n\n\n<p>5<sup>7<\/sup> . 5<sup>-2<\/sup><\/p>\n\n\n\n<p>5<sup>7+ -2 <\/sup>   Use the identity a<sup>x<\/sup> a<sup>y<\/sup> = a  <sup>x+y<\/sup><\/p>\n\n\n\n<p>5<sup>5<\/sup><\/p>\n\n\n\n<p>So,&nbsp;5<sup>7<\/sup> . 5<sup>-2<\/sup> &nbsp;is equal to 5<sup>5<\/sup>.<\/p>\n\n\n\n<p>Step 2: Now write each answer choice in the form 5<\/p>\n\n\n\n<p>Write 1 \/ 5<sup>-5<\/sup> in the form&nbsp; 5<\/p>\n\n\n\n<p>1 \/ 5<sup>-5<\/sup> <\/p>\n\n\n\n<p>5<sup>-(-5)<\/sup>    Use&nbsp;the identity 1\/a<sup>x <\/sup> = a<sup>-x<\/sup><\/p>\n\n\n\n<p>5<sup>5<\/sup><\/p>\n\n\n\n<p>Both&nbsp;1 \/ 5<sup>-5<\/sup> and&nbsp;5<sup>7<\/sup> . 5<sup>-2<\/sup> are equal to 5<sup>5<\/sup> <\/p>\n\n\n\n<p>The&nbsp;expressions  1 \/ 5<sup>-5<\/sup>  and&nbsp;5<sup>7<\/sup> . 5<sup>-2<\/sup> are equivalent.<\/p>\n\n\n\n<p>Write&nbsp;1 \/ 5<sup>5<\/sup> in the form 5<\/p>\n\n\n\n<p>1 \/ 5<sup>5<\/sup><\/p>\n\n\n\n<p>=5<sup>-5 <\/sup> Use&nbsp;the identity 1 \/ a<sup>x <\/sup> = a<sup>-x<\/sup><\/p>\n\n\n\n<p>So,1 \/ 5<sup>5<\/sup> is equal to 5<sup>-5 <\/sup> , but&nbsp; 5<sup>7<\/sup> . 5<sup>-2<\/sup> is not. (It is equal to5<sup>5<\/sup>)<\/p>\n\n\n\n<p>The&nbsp;expressions 1 \/ 5<sup>5<\/sup> and&nbsp; 5<sup>7<\/sup> . 5<sup>-2<\/sup> are not equivalent.<\/p>\n\n\n\n<p>Write&nbsp; 1 \/ 5<sup>-14<\/sup>  in the form 5<\/p>\n\n\n\n<p>1 \/ 5<sup>-14<\/sup> <\/p>\n\n\n\n<p>= 5<sup>-(-14)<\/sup>   Use&nbsp;the identity 1 \/ a<sup>x <\/sup> = a<sup>-x<\/sup><\/p>\n\n\n\n<p>= 5<sup>14<\/sup><\/p>\n\n\n\n<p>So,&nbsp;1 \/ 5<sup>-14<\/sup>  is equal to  5<sup>14<\/sup> ,&nbsp;but 5<sup>7<\/sup> . 5<sup>-2<\/sup>  is not. (It is equal to&nbsp;5<sup>5<\/sup> )<\/p>\n\n\n\n<p>The&nbsp;expressions 1 \/ 5<sup>-14<\/sup>    and&nbsp; 5<sup>7<\/sup> . 5<sup>-2<\/sup>are not equivalent.<\/p>\n\n\n\n<p>The&nbsp;expression&nbsp; 5<sup>-14<\/sup> is in the form 5 . You&#8217;ve already found that 5<sup>7<\/sup> . 5<sup>-2<\/sup> is not equal to 5<sup>-14<\/sup>(It is equal to&nbsp;5<sup>5<\/sup>.)<\/p>\n\n\n\n<p>The&nbsp;expressions&nbsp;5<sup>-14<\/sup> and&nbsp;5<sup>7<\/sup> . 5<sup>-2<\/sup> are not equivalent.<\/p>\n\n\n\n<p>The&nbsp;correct answers&nbsp;is 1 \/ 5<sup>-5<\/sup> .<\/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\/79947\/487\/703\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-131.png\" alt=\"\" class=\"wp-image-8094\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-131.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-131-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-131-150x150.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\/79804\/140\/976\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-140.png\" alt=\"\" class=\"wp-image-8095\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-140.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-140-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-140-150x150.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 : Understanding Equivalent Expressions Key Properties of Exponents Identifying Equivalent Expressions Examples: Learn with an example Select all the expressions that are equivalent to 103 . 10-8 To&nbsp;find which expressions are equivalent to 103 .10-8 , write each expression with the same base. The answer choices and 103<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/u-9-identify-equivalent-expressions-involving-exponents\/\">Continue reading <span class=\"screen-reader-text\">&#8220;U.9 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-357","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/357","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=357"}],"version-history":[{"count":16,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/357\/revisions"}],"predecessor-version":[{"id":15658,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/357\/revisions\/15658"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=357"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}