{"id":102,"date":"2022-04-12T12:06:59","date_gmt":"2022-04-12T12:06:59","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=102"},"modified":"2025-10-09T05:31:43","modified_gmt":"2025-10-09T05:31:43","slug":"f-7-evaluate-negative-exponents","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/f-7-evaluate-negative-exponents\/","title":{"rendered":"F.7 Evaluate negative exponents"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Evaluate negative 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<p class=\"has-primary-color has-text-color has-link-color has-large-font-size wp-elements-8ca2006c77b24f9e53dd21ba70c16a79\">\ud83c\udf1f <strong>Evaluate Negative Exponents<\/strong> \ud83c\udf1f<\/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 What Are Exponents?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>An <strong>exponent<\/strong> shows how many times a number (called the <strong>base<\/strong>) is multiplied by itself.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\ud83d\udc49 <strong>Example<\/strong>: 2<sup>3<\/sup>=2\u00d72\u00d72=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>\ud83d\udd39 What Are Negative Exponents?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>A <strong>negative exponent<\/strong> means <strong>take the reciprocal<\/strong> (flip the base) and <strong>make the exponent positive<\/strong>.<\/p>\n\n\n\n<p><strong>\ud83d\udc49 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<\/ul>\n\n\n\n<p>\ud83e\udde0 <strong>Rule:<\/strong> <\/p>\n\n\n\n<p class=\"has-text-align-center\">a<sup>\u2212n<\/sup>=1\/a<sup>n<\/sup> (where a\u22600)<\/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 Examples<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li>5<sup>\u22122<\/sup>=1\/5<sup>2<\/sup>=1\/25<\/li>\n\n\n\n<li>10<sup>\u22121<\/sup>=1\/10<sup>1<\/sup>=1\/10<\/li>\n\n\n\n<li>(2\/3)<sup>\u22122<\/sup>=(3\/2)<sup>2<\/sup>=9\/4\u200b<\/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>\ud83d\udd39 Important Properties of Exponents<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>1. Product of powers:<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\">a<sup>m<\/sup>\u00d7a<sup>n<\/sup>=a<sup>m+n<\/sup><\/p>\n\n\n\n<p><strong>2. Quotient of powers:<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\">a<sup>m<\/sup>\/a<sup>n<\/sup>=a<sup>m\u2212n<\/sup><\/p>\n\n\n\n<p><strong>3. Power of a power:<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\">(a<sup>m<\/sup>)<sup>n<\/sup>=a<sup>m\u00d7n<\/sup><\/p>\n\n\n\n<p><strong>4. Zero exponent:<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\">a<sup>0<\/sup>=1 (where a\u22600)<\/p>\n\n\n\n<p><strong>5. Negative exponent:<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\">a<sup>\u2212n<\/sup>=1\/a<sup>n<\/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 Real-Life Application \ud83c\udf0d<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Negative exponents are used in:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Scientific notation<\/strong> for small numbers:<br>2.5\u00d710<sup>\u22123<\/sup>=0.0025<\/li>\n\n\n\n<li><strong>Physics and Chemistry<\/strong> to represent very small quantities like charge, mass, or wavelength.<\/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 Quick Tip \ud83d\udca1<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Always remember:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Negative exponents <strong>don\u2019t make the value negative<\/strong>,<\/li>\n\n\n\n<li>they just <strong>flip the fraction<\/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\udde9 <strong>Practice Problems<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li>3<sup>\u22122<\/sup>=?<\/li>\n\n\n\n<li>1\/4<sup>\u22123<\/sup>=?<\/li>\n\n\n\n<li>(5<sup>2<\/sup>)<sup>\u22121<\/sup>=?<\/li>\n\n\n\n<li>2<sup>\u22124<\/sup>\u00d72<sup>3<\/sup>=?<\/li>\n\n\n\n<li>(1\/2)<sup>\u22122<\/sup>=?<\/li>\n<\/ol>\n\n\n\n<p class=\"has-text-align-center has-text-color has-huge-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-5354a5c044741b694ac24529cce4aba6\" style=\"background-color:#ce9cff\"><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-7525c42e5e1f9b743580b441630adc47\" 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 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\">\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\/2022\/10\/Untitled_design__12_-removebg-preview.png\" alt=\"\" class=\"wp-image-2916\" style=\"width:210px;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-88ff964ff702eeea94072269af1b4d6c\" style=\"background-color:#ffaa9c\"><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\">\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\/2022\/10\/Untitled_design__13_-removebg-preview.png\" alt=\"\" class=\"wp-image-2921\" style=\"width:166px;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-17b319920388efbffa4e1892b1e77618\" style=\"background-color:#d8f192\"><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-42cf38310fea3b23d06765318af5d87b\" style=\"color:#b00012\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p><strong>Evaluate. Write your answer as a fraction or whole number without exponents.<\/strong><\/p>\n\n\n\n<p>                    3<sup>\u20133<\/sup> =<\/p>\n<\/div><\/div>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"207\" height=\"219\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/16-removebg-preview-1.png\" alt=\"\" class=\"wp-image-10270\" style=\"aspect-ratio:0.946875;width:312px;height:auto\"\/><\/figure>\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\"><a href=\"https:\/\/wordwall.net\/play\/78112\/937\/414\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-291.png\" alt=\"\" class=\"wp-image-9564\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-291.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-291-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-291-150x150.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\/33848\/098\/900\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-298.png\" alt=\"\" class=\"wp-image-9565\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-298.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-298-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-298-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Evaluate negative exponents Key Notes : \ud83c\udf1f Evaluate Negative Exponents \ud83c\udf1f \ud83d\udd39 What Are Exponents? An exponent shows how many times a number (called the base) is multiplied by itself. \ud83d\udd39 What Are Negative Exponents? A negative exponent means take the reciprocal (flip the base) and make the exponent positive. \ud83d\udc49 Example: \ud83e\udde0 Rule: a\u2212n=1\/an<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/f-7-evaluate-negative-exponents\/\">Continue reading <span class=\"screen-reader-text\">&#8220;F.7 Evaluate 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-102","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\/102","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=102"}],"version-history":[{"count":22,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/102\/revisions"}],"predecessor-version":[{"id":21774,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/102\/revisions\/21774"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=102"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}