{"id":92,"date":"2022-04-12T12:05:36","date_gmt":"2022-04-12T12:05:36","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=92"},"modified":"2025-10-29T06:07:20","modified_gmt":"2025-10-29T06:07:20","slug":"f-2-evaluate-exponents","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/f-2-evaluate-exponents\/","title":{"rendered":"F.2 Evaluate exponents"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Evaluate 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 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 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 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\/DAG3JQk1oJo\/ERwbq4zPRPd_Rbu4EHGDdQ\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAG3JQk1oJo&#x2F;ERwbq4zPRPd_Rbu4EHGDdQ&#x2F;watch?utm_content=DAG3JQk1oJo&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<\/div>\n<\/div>\n<\/div>\n<\/div>\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<figure class=\"wp-block-table has-normal-font-size\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>\ud83d\udd39 What is an Exponent?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>An <strong>exponent<\/strong> tells us how many times a number (the base) is multiplied by itself.<\/li>\n\n\n\n<li>General form: a<sup>n<\/sup>=a\u00d7a\u00d7a\u2026\u00d7a (n&nbsp;times)<\/li>\n\n\n\n<li>a \u2192 base<\/li>\n\n\n\n<li>n \u2192 exponent (or power)<\/li>\n\n\n\n<li><strong>Example:<\/strong> 3<sup>4<\/sup>=3\u00d73\u00d73\u00d73=81<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table has-normal-font-size\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>\ud83d\udd39 Important Rules of Exponents<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Product of Powers Rule:<\/strong> <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a<sup>m<\/sup>\u00d7a<sup>n<\/sup>=a<sup>m+n<\/sup><\/li>\n\n\n\n<li>Example: 2<sup>3<\/sup>\u00d72<sup>4<\/sup>=2<sup>7<\/sup>=128<\/li>\n<\/ul>\n\n\n\n<p><strong>Quotient of Powers Rule:<\/strong> <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a<sup>m<\/sup>\/a<sup>n<\/sup>=a<sup>m\u2212n<\/sup> (a\u22600)<\/li>\n\n\n\n<li> Example: 5<sup>6<\/sup>\/5<sup>2<\/sup>=5<sup>4<\/sup>=625<\/li>\n<\/ul>\n\n\n\n<p><strong>Power of a Power Rule:<\/strong> <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(a<sup>m<\/sup>)<sup>n<\/sup>=a<sup>m\u22c5n<\/sup> <\/li>\n\n\n\n<li>Example: (3<sup>2<\/sup>)<sup>4<\/sup>=3<sup>8<\/sup>=6561<\/li>\n<\/ul>\n\n\n\n<p><strong>Power of a Product Rule:<\/strong> <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(ab)<sup>n<\/sup>=a<sup>n<\/sup>.b<sup>n<\/sup> <\/li>\n\n\n\n<li>Example: (2\u00d73)<sup>4<\/sup>=2<sup>4<\/sup>\u00d73<sup>4<\/sup>=16\u00d781=1296<\/li>\n<\/ul>\n\n\n\n<p><strong>Power of a Quotient Rule:<\/strong> <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(a\/b)<sup>n<\/sup>=a<sup>n<\/sup>\/b<sup>n<\/sup> (b\u22600)<\/li>\n\n\n\n<li>Example: (4\/5)<sup>2<\/sup>=16\/25\u200b<\/li>\n<\/ul>\n\n\n\n<p><strong>Zero Exponent Rule:<\/strong> <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a<sup>0<\/sup>=1 (a\u22600)<\/li>\n\n\n\n<li> Example: 7<sup>0<\/sup>=1<\/li>\n<\/ul>\n\n\n\n<p><strong>Negative Exponent Rule:<\/strong> <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a<sup>\u2212n<\/sup>=1\/a<sup>n<\/sup> (a\u22600)<\/li>\n\n\n\n<li>Example: 2<sup>\u22123<\/sup>=1\/2<sup>3<\/sup>=1\/8<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table has-normal-font-size\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>\ud83d\udd39 Evaluating Exponents (Examples)<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2<sup>5<\/sup>=2\u00d72\u00d72\u00d72\u00d72=32<\/li>\n\n\n\n<li>(5<sup>3<\/sup>)<sup>2<\/sup>=5<sup>6<\/sup>=15625<\/li>\n\n\n\n<li>7<sup>4<\/sup>\/7<sup>2<\/sup>=7<sup>4\u22122<\/sup>=7<sup>2<\/sup>=49<\/li>\n\n\n\n<li>10<sup>\u22122<\/sup>=1\/10<sup>2<\/sup>=1\/100<\/li>\n\n\n\n<li>(3\u00d72)<sup>3<\/sup>=3<sup>3<\/sup>\u00d72<sup>3<\/sup>=27\u00d78=216<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table has-normal-font-size\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>\ud83d\udd39  Common Mistakes to Avoid<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-text-align-center\">a<sup>m<\/sup>+a<sup>n<\/sup>\u2260a<sup>m+n<\/sup><\/p>\n\n\n\n<p class=\"has-text-align-center\">(a+b)<sup>2<\/sup>\u2260a<sup>2<\/sup>+b<sup>2<\/sup>  (it is a<sup>2<\/sup>+2ab+b<sup>2<\/sup>)<\/p>\n\n\n\n<p>Negative sign matters:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(\u22122)<sup>4<\/sup>=16<\/li>\n\n\n\n<li>\u22122<sup>4<\/sup>=\u221216<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table has-normal-font-size\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>\ud83d\udd39  Real-Life Applications of Exponents<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Scientific notation (large and small numbers).<\/li>\n\n\n\n<li>Growth and decay problems (population growth, bacteria growth, radioactive decay).<\/li>\n\n\n\n<li>Area and volume calculations.<\/li>\n\n\n\n<li>Computer science (binary numbers and memory size like KB, MB, GB).<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table has-normal-font-size\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>\u2705 <strong>Summary:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Exponents are repeated multiplication.<\/li>\n\n\n\n<li>Learn and apply exponent rules correctly.<\/li>\n\n\n\n<li>Be careful with signs, brackets, and negative powers.<\/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-background-color has-text-color has-background has-link-color has-normal-font-size wp-elements-fd71ae15a8fbd2ae23b5e08a48560322\" style=\"background-color:#820000\"><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-c273211fa00f0367261f692c0f83d41b\" style=\"color:#d90000\">\u2708\ufe0f Evaluate. <\/p>\n\n\n\n<p>9<sup>2<\/sup> =<\/p>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The base is 9 and the exponent is 2. Use 9 as a factor 2 times.<\/li>\n\n\n\n<li>9<sup>2<\/sup> = 9 \u00b7 9<\/li>\n\n\n\n<li>= 81<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background-color has-text-color has-background has-link-color has-normal-font-size wp-elements-97df5c1e68828a9ff48ab82967805045\" style=\"background-color:#070066\"><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-c273211fa00f0367261f692c0f83d41b\" style=\"color:#d90000\">\u2708\ufe0f Evaluate. <\/p>\n\n\n\n<p>4<sup>3<\/sup> =<\/p>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The base is 4 and the exponent is 3. Use 4 as a factor 3 times.<\/li>\n\n\n\n<li>4<sup>3<\/sup> = 4 \u00b7 4 \u00b7 4<\/li>\n\n\n\n<li>= 64<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background-color has-text-color has-background has-link-color has-normal-font-size wp-elements-19c5177cacea73e007efa4700bcf6290\" style=\"background-color:#006c7d\"><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-c273211fa00f0367261f692c0f83d41b\" style=\"color:#d90000\">\u2708\ufe0f Evaluate. <\/p>\n\n\n\n<p>6<sup>2<\/sup> =<\/p>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The base is 6 and the exponent is 2. Use 6 as a factor 2 times.<\/li>\n\n\n\n<li>6<sup>2<\/sup> = 6 \u00b7 6<\/li>\n\n\n\n<li>= 36<\/li>\n<\/ul>\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\/77127\/696\/792\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-296.png\" alt=\"\" class=\"wp-image-9580\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-296.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-296-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-296-150x150.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\/77037\/183\/266\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-303.png\" alt=\"\" class=\"wp-image-9581\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-303.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-303-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-303-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Evaluate exponents Design by Delta publications Key Notes : \ud83d\udd39 What is an Exponent? \ud83d\udd39 Important Rules of Exponents Product of Powers Rule: Quotient of Powers Rule: Power of a Power Rule: Power of a Product Rule: Power of a Quotient Rule: Zero Exponent Rule: Negative Exponent Rule: \ud83d\udd39 Evaluating Exponents (Examples) \ud83d\udd39 Common Mistakes<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/f-2-evaluate-exponents\/\">Continue reading <span class=\"screen-reader-text\">&#8220;F.2 Evaluate 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-92","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\/92","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=92"}],"version-history":[{"count":35,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/92\/revisions"}],"predecessor-version":[{"id":22043,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/92\/revisions\/22043"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=92"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}