{"id":100,"date":"2022-04-12T12:06:41","date_gmt":"2022-04-12T12:06:41","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=100"},"modified":"2025-10-29T06:52:20","modified_gmt":"2025-10-29T06:52:20","slug":"f-6-understanding-negative-exponents","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/f-6-understanding-negative-exponents\/","title":{"rendered":"F.6 Understanding negative exponents"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Understanding negative 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\/DAG3JtO_XtA\/qXZhyPwuPFySr6zbyQlI0A\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAG3JtO_XtA&#x2F;qXZhyPwuPFySr6zbyQlI0A&#x2F;watch?utm_content=DAG3JtO_XtA&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-a5e808d1afb5db4c29a49d31ed035cf5\"><strong>\ud83d\udcd8 Understanding Negative 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>An <strong>exponent<\/strong> tells us <strong>how many times a number (base) is multiplied by itself<\/strong>.<\/p>\n\n\n\n<p><strong>Example: <\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\">3<sup>4<\/sup>=3\u00d73\u00d73\u00d73=81<\/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>What is a negative exponent?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>A <strong>negative exponent<\/strong> means that the number is <strong>reciprocal<\/strong> (1 divided by the number with a positive exponent).<\/p>\n\n\n\n<p><strong>Rule:<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\"> a<sup>\u2212n<\/sup>=1\/a<sup>n<\/sup>(where&nbsp;a\u22600)<\/p>\n\n\n\n<p><strong>Example: <\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2<sup>\u22123<\/sup>=1\/2<sup>3<\/sup>=1\/8<\/li>\n\n\n\n<li>5<sup>\u22122<\/sup>=1\/5<sup>2<\/sup>=1\/25<\/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>Why do negative exponents work?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Exponents follow the <strong>division rule<\/strong>:<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\">a<sup>m<\/sup>\u00f7a<sup>n<\/sup>=a<sup>m\u2212n<\/sup><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If m&lt;n, the exponent becomes negative:<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\">a<sup>2<\/sup>\u00f7a<sup>5<\/sup>=a<sup>2\u22125<\/sup>=a<sup>\u22123<\/sup>=1\/a<sup>3<\/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>Properties of Negative Exponents<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Property<\/th><th>Explanation<\/th><th>Example<\/th><\/tr><\/thead><tbody><tr><td><strong>Reciprocal Rule<\/strong><\/td><td>a<sup>\u2212n<\/sup>=1\/a<sup>n<\/sup><\/td><td>3<sup>\u22122<\/sup>=1\/9<\/td><\/tr><tr><td><strong>Product Rule<\/strong><\/td><td>a<sup>\u2212m<\/sup>\u22c5a<sup>\u2212n<\/sup>=a<sup>\u2212(m+n)<\/sup><\/td><td>2<sup>\u22122<\/sup>\u22c52<sup>\u22123<\/sup>=2<sup>\u22125<\/sup>=1\/32<\/td><\/tr><tr><td><strong>Quotient Rule<\/strong><\/td><td>a<sup>\u2212m<\/sup>\/a<sup>\u2212n<\/sup>=a<sup>-(m\u2212n)<\/sup> =a<sup>n\u2212m<\/sup><\/td><td>2<sup>\u22123<\/sup>\/2<sup>\u22125<\/sup>=2<sup>2<\/sup>=4<\/td><\/tr><tr><td><strong>Power Rule<\/strong><\/td><td>(a<sup>\u2212m<\/sup>)<sup>n<\/sup>=a<sup>\u2212mn<\/sup><\/td><td>(3<sup>\u22122<\/sup>)<sup>3<\/sup>=3<sup>\u22126<\/sup>=1\/729<\/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><strong>Negative Exponents with Fractions<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If the base is a fraction:<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\">(a\/b)<sup>\u2212n<\/sup>=(b\/a)<sup>n<\/sup><\/p>\n\n\n\n<p><strong>Example<\/strong>:<\/p>\n\n\n\n<p class=\"has-text-align-center\"> (2\/3)<sup>\u22122<\/sup>=(3\/2)<sup>2<\/sup>=9\/4<\/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>Quick Tips \u2705<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A negative exponent <strong>flips the base<\/strong> (reciprocal) and makes the exponent positive.<\/li>\n\n\n\n<li>a<sup>0<\/sup>=1 for any a\u22600.<\/li>\n\n\n\n<li>Always <strong>write your final answer as a positive exponent<\/strong> when possible.<\/li>\n<\/ul>\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-primary-color has-text-color has-background has-link-color has-normal-font-size wp-elements-5d0d0dc384bccc18087406536d758a80\" style=\"background-color:#e4fe9c\"><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-6af30c12252c42712d8a0dedf4833cfe\" style=\"color:#b00012\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-normal-font-size\"><strong>Write&nbsp;the expression as a fraction with a positive exponent. Do not evaluate the&nbsp;expression.<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\">9<sup>-2<\/sup><\/p>\n<\/div><\/div>\n\n\n\n<p>The&nbsp;base has a negative exponent,&nbsp;\u20132.&nbsp;You can rewrite the expression as a fraction with a numerator of 1 and a positive exponent,&nbsp;2,&nbsp;in the&nbsp;denominator.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/10\/Untitled_design__12_-removebg-preview.png\" alt=\"\" class=\"wp-image-2916\" style=\"width:178px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/10\/Untitled_design__12_-removebg-preview.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/10\/Untitled_design__12_-removebg-preview-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/10\/Untitled_design__12_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div><\/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-43ee26d5ff99cd844bde9873354ca47b\" style=\"background-color:#9ca2ff\"><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-bfaa91472a5e96ed8f2b6b10b7b0a85c\" style=\"color:#b00012\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p><strong>Write&nbsp;the expression as a whole number with a negative exponent. Do not evaluate the&nbsp;expression.<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\">1\/<em>7<sup>3<\/sup><\/em><\/p>\n<\/div><\/div>\n\n\n\n<p>There&nbsp;is a positive exponent,&nbsp;3,&nbsp;in the denominator. You can rewrite the expression with an exponent of&nbsp;\u20133&nbsp;instead.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/10\/Untitled_design__13_-removebg-preview.png\" alt=\"\" class=\"wp-image-2921\" style=\"width:182px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/10\/Untitled_design__13_-removebg-preview.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/10\/Untitled_design__13_-removebg-preview-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/10\/Untitled_design__13_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div><\/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-90ed53616bff5ce84f8aab3f3e1c5c25\" style=\"background-color:#f6dcdc\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-background-background-color has-text-color has-background has-link-color has-normal-font-size wp-elements-b148feb3ff314e39781f7a483c0e0f71\" style=\"color:#b00012\"><strong>Write the expression as a fraction with a positive exponent. Do not evaluate the expression.<br><\/strong>5<sup>\u20133<\/sup><\/p>\n\n\n\n<p class=\"has-normal-font-size\">The&nbsp;base has a negative exponent,&nbsp;\u20133.&nbsp;You can rewrite the expression as a fraction with a numerator of 1 and a positive exponent,&nbsp;3,&nbsp;in the&nbsp;denominator.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/09\/Untitled_design__1_-removebg-preview.png\" alt=\"\" class=\"wp-image-11711\" style=\"width:138px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/09\/Untitled_design__1_-removebg-preview.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/09\/Untitled_design__1_-removebg-preview-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/09\/Untitled_design__1_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div><\/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\"><a href=\"https:\/\/wordwall.net\/play\/78112\/044\/675\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-292.png\" alt=\"\" class=\"wp-image-9568\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-292.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-292-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-292-150x150.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\/36169\/170\/299\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-299.png\" alt=\"\" class=\"wp-image-9569\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-299.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-299-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-299-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Understanding negative exponents Design by Delta publications Key Notes : \ud83d\udcd8 Understanding Negative Exponents What is an exponent? An exponent tells us how many times a number (base) is multiplied by itself. Example: 34=3\u00d73\u00d73\u00d73=81 What is a negative exponent? A negative exponent means that the number is reciprocal (1 divided by the number with a<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/f-6-understanding-negative-exponents\/\">Continue reading <span class=\"screen-reader-text\">&#8220;F.6 Understanding negative 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-100","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\/100","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=100"}],"version-history":[{"count":31,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/100\/revisions"}],"predecessor-version":[{"id":22047,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/100\/revisions\/22047"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=100"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}