{"id":106,"date":"2022-04-12T12:07:38","date_gmt":"2022-04-12T12:07:38","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=106"},"modified":"2025-10-29T09:22:24","modified_gmt":"2025-10-29T09:22:24","slug":"f-9-division-with-exponents","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/f-9-division-with-exponents\/","title":{"rendered":"F.9 Division with exponents"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Division with 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\/DAG3KXWp3dM\/NEUA8uDh1wyPVP0nhd_9Ow\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAG3KXWp3dM&#x2F;NEUA8uDh1wyPVP0nhd_9Ow&#x2F;watch?utm_content=DAG3KXWp3dM&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<p class=\"has-primary-color has-text-color has-link-color has-large-font-size wp-elements-594a23ab92740fa5362e73da485a92cb\"><strong>\ud83d\udcd8 Division with Exponents<\/strong><\/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>\ud83d\udd39 Rule of Division with Same Bases<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>When dividing numbers with the same base, <strong>subtract the exponents<\/strong>.<\/p>\n\n\n\n<p>\ud83d\udc49 <strong>Rule:<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>a\u1d50 \u00f7 a\u207f = a\u1d50\u207b\u207f<\/strong><\/p>\n\n\n\n<p>(Where <em>a<\/em> is the base, <em>m<\/em> and <em>n<\/em> are exponents)<\/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>\ud83d\udd39 <strong>Examples<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>1\ufe0f\u20e3 <strong>x\u2075 \u00f7 x\u00b2 = x\u2075\u207b\u00b2 = x\u00b3<\/strong><\/p>\n\n\n\n<p>2\ufe0f\u20e3 <strong>7\u2074 \u00f7 7\u00b2 = 7\u2074\u207b\u00b2 = 7\u00b2 = 49<\/strong><\/p>\n\n\n\n<p>3\ufe0f\u20e3 <strong>a\u2076 \u00f7 a\u2076 = a\u2076\u207b\u2076 = a\u2070 = 1<\/strong><\/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>\u2699\ufe0f <strong>Bases Must Be the Same<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>This rule works <strong>only when the bases are the same<\/strong>.<br>If the bases are different, you <strong>cannot<\/strong> apply the exponent rule.<\/p>\n\n\n\n<p>\ud83d\udeab <strong>Example (cannot simplify):<\/strong> <\/p>\n\n\n\n<p class=\"has-text-align-center\">3<sup>4<\/sup>\/2<sup>4<\/sup>&nbsp;\u2192&nbsp;Bases&nbsp;are&nbsp;different.<\/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>\ud83d\udca1 <strong>Zero and Negative Exponents<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>If the exponent becomes <strong>zero<\/strong> or <strong>negative<\/strong> after subtraction, apply these rules:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a<sup>0<\/sup>=1<\/li>\n\n\n\n<li>a<sup>\u2212n<\/sup>=1\/a<sup>n<\/sup><\/li>\n<\/ul>\n\n\n\n<p>\u2705 <strong>Example 1:<\/strong> 7<sup>3<\/sup>\/7<sup>3<\/sup>=7<sup>3\u22123<\/sup>=7<sup>0<\/sup>=1<\/p>\n\n\n\n<p>\u2705 <strong>Example 2:<\/strong> 4<sup>2<\/sup>\/4<sup>5<\/sup>=4<sup>2\u22125<\/sup>=4<sup>\u22123<\/sup>=1\/4<sup>3<\/sup>=1\/64<\/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>\ud83e\udde9 <strong>Division of Coefficients and Powers<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>When dividing numbers with exponents <strong>and coefficients<\/strong>,<br><strong>divide the coefficients<\/strong> and <strong>apply the exponent rule<\/strong> to the powers.<\/p>\n\n\n\n<p>\u2705 <strong>Example:<\/strong> <\/p>\n\n\n\n<p class=\"has-text-align-center\">8X<sup>6<\/sup>\/4X<sup>2<\/sup>=8\/4\u00d7X<sup>6\u22122<\/sup> =2X<sup>4<\/sup> <\/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>\ud83d\udcd8 <strong>Division of Powers with Power<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>If a power is divided and both have exponents raised again, apply both rules step by step.<\/p>\n\n\n\n<p>\u2705 <strong>Example:<\/strong> <\/p>\n\n\n\n<p class=\"has-text-align-center\">(a<sup>3<\/sup>)<sup>4<\/sup>\/(a<sup>3<\/sup>)<sup>2<\/sup>=a<sup>(3\u00d74)\u2212(3\u00d72)<\/sup>=a<sup>12\u22126<\/sup>=a<sup>6<\/sup><\/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>\ud83d\udd39 <strong>Important Notes<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2728 Bases <strong>must be the same<\/strong> to apply the rule.<\/li>\n\n\n\n<li>\u2728 If the <strong>base is different<\/strong>, divide normally (do not subtract exponents).<\/li>\n\n\n\n<li>\u2728 Any non-zero number raised to the power of <strong>0 equals 1<\/strong>.<\/li>\n\n\n\n<li>\u2728 When the <strong>exponent becomes negative<\/strong>, rewrite it using a reciprocal:<\/li>\n\n\n\n<li><strong>a\u207b\u207f = 1 \/ a\u207f<\/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><strong>\ud83d\udd39 <strong>More Examples<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\ud83d\udcd8 <strong>Example 1:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>m\u2079 \u00f7 m\u2074 = m\u2075<\/strong><\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udcd8 <strong>Example 2:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>(2\u2076 \u00f7 2\u00b3) = 2\u00b3 = 8<\/strong><\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udcd8 <strong>Example 3:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>(a\u00b3b\u00b2) \u00f7 (a\u00b2b) = a\u00b3\u207b\u00b2 b\u00b2\u207b\u00b9 = ab<\/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><strong>\ud83d\udd39 <strong>Word Problems<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\ud83e\udde9 <strong>Example:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If the area of a square is 5\u2076 cm\u00b2 and the side length is 5\u00b3 cm,<\/li>\n\n\n\n<li>find the missing exponent for the side.<\/li>\n<\/ul>\n\n\n\n<p>Solution:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Area \u00f7 side = 5\u2076 \u00f7 5\u00b3 = 5\u00b3<\/li>\n\n\n\n<li>\u2705 <strong>Each side = 5\u00b3 cm<\/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><strong>\ud83d\udd39 <strong>Quick Summary Table<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Expression<\/th><th>Simplified Form<\/th><th>Rule Used<\/th><\/tr><\/thead><tbody><tr><td>a\u2077 \u00f7 a\u00b2<\/td><td>a\u2075<\/td><td>Subtract exponents<\/td><\/tr><tr><td>4\u2075 \u00f7 4\u00b3<\/td><td>4\u00b2<\/td><td>Subtract exponents<\/td><\/tr><tr><td>a\u2075 \u00f7 a\u2075<\/td><td>1<\/td><td>a\u2070 = 1<\/td><\/tr><tr><td>a\u00b3 \u00f7 a\u2076<\/td><td>a\u207b\u00b3 = 1\/a\u00b3<\/td><td>Negative exponent rule<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\ud83d\udca1 <strong>Tip:<\/strong> Always check the base first! Only subtract exponents when <strong>bases are identical<\/strong>.<\/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>\u2728 <strong>In short:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Division with Exponents = Same Base \u2192 Subtract Powers<\/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><strong>\ud83e\udde0 <strong>Memory Trick:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\ud83d\udc49 &#8220;When you divide powers, just subtract the towers!&#8221;<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-link-color has-large-font-size wp-elements-3fefd20f8ce119a518e5f53333ab5486\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\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-950752689fe3d6ff61d0c30bdb378cc4\" style=\"background-color:#ceb9f9\"><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-28b27ee28f694c8bd8709e49d8bfcb3a\" 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 as a single term, without a&nbsp;denominator.<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\">j<sup>5<\/sup> \/ j<sup>8<\/sup><\/p>\n<\/div><\/div>\n\n\n\n<p>Simplify.<\/p>\n\n\n\n<p class=\"has-normal-font-size\">j<sup>5<\/sup> \/ j<sup>8<\/sup> = j <sup>5-8<\/sup><\/p>\n\n\n\n<p class=\"has-normal-font-size\">Divide,&nbsp;remembering to subtract the&nbsp;exponents<\/p>\n\n\n\n<p class=\"has-normal-font-size\">           = j<sup>-3<\/sup><\/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-97d2101951afd34cd582cadbb7cb29b3\" style=\"background-color:#f2f297\"><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-ed7f3cc6e3419c2035a8d54a335c4622\" 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 as a single term, without a&nbsp;denominator.<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\">p<sup>7<\/sup> \/p<sup>2<\/sup><\/p>\n<\/div><\/div>\n\n\n\n<p>Simplify.<\/p>\n\n\n\n<p>p<sup>7<\/sup> \/p<sup>2<\/sup> = p<sup>7-2<\/sup><\/p>\n\n\n\n<p class=\"has-normal-font-size\"><em>Divide,&nbsp;remembering to subtract the&nbsp;exponents<\/em><\/p>\n\n\n\n<p class=\"has-normal-font-size\">           = p<sup>5<\/sup><\/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-a881fcf2406c3724a6ebbb0da3f68c64\" style=\"background-color:#93f1b2\"><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-c9291caae98c97540077947a4954777a\" 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 as a single term, without a&nbsp;denominator.<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\">k<sup>10<\/sup> \/k<sup>12<\/sup><\/p>\n<\/div><\/div>\n\n\n\n<p>Simplify.<\/p>\n\n\n\n<p>k<sup>10<\/sup> \/k<sup>12<\/sup> = k<sup>10-12<\/sup><\/p>\n\n\n\n<p class=\"has-normal-font-size\"><em>Divide,&nbsp;remembering to subtract the&nbsp;exponents<\/em><\/p>\n\n\n\n<p class=\"has-normal-font-size\">           = k<sup>-2<\/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!\ud83d\udd8a\ufe0f<\/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\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-303.png\" alt=\"\" class=\"wp-image-9607\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-303.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-303-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-303-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/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\/33892\/822\/477\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-310.png\" alt=\"\" class=\"wp-image-9608\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-310.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-310-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-310-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Division with exponents Design by Delta publications Key Notes : \ud83d\udcd8 Division with Exponents \ud83d\udd39 Rule of Division with Same Bases When dividing numbers with the same base, subtract the exponents. \ud83d\udc49 Rule: a\u1d50 \u00f7 a\u207f = a\u1d50\u207b\u207f (Where a is the base, m and n are exponents) \ud83d\udd39 Examples 1\ufe0f\u20e3 x\u2075 \u00f7 x\u00b2 =<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/f-9-division-with-exponents\/\">Continue reading <span class=\"screen-reader-text\">&#8220;F.9 Division with 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-106","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\/106","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=106"}],"version-history":[{"count":28,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/106\/revisions"}],"predecessor-version":[{"id":22052,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/106\/revisions\/22052"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=106"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}