{"id":104,"date":"2022-04-12T12:07:15","date_gmt":"2022-04-12T12:07:15","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=104"},"modified":"2025-10-29T09:08:07","modified_gmt":"2025-10-29T09:08:07","slug":"f-8-multiplication-with-exponents","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/f-8-multiplication-with-exponents\/","title":{"rendered":"F.8 Multiplication with exponents"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Multiplication 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 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\/DAG3KEwL3fI\/Nv5-InNtgk3OBceQbYxRhA\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAG3KEwL3fI&#x2F;Nv5-InNtgk3OBceQbYxRhA&#x2F;watch?utm_content=DAG3KEwL3fI&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\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<h3 class=\"wp-block-heading has-primary-color has-text-color has-link-color has-large-font-size wp-elements-ab73faccee656cd2bb81c7836ef8a6c7\"><strong>Multiplication with Exponents \ud83d\udcda\u2728<\/strong><\/h3>\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 are exponents?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>An <strong>exponent<\/strong> tells us <strong>how many times a number is multiplied by itself<\/strong>.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><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><strong>Multiplying numbers with the same base<\/strong> \ud83d\udd17<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Rule:<\/strong> When multiplying powers with the same base, <strong>add their exponents<\/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>Example:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>3<sup>2<\/sup>\u00d73<sup>4<\/sup>=3<sup>2+4<\/sup>=3<sup>6<\/sup>=729<\/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><strong>Multiplying numbers with different bases<\/strong> \u26a1<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Rule:<\/strong> If the bases are different, <strong>you cannot add the exponents<\/strong>. Multiply the numbers separately.<\/p>\n\n\n\n<p><strong>Example:<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\">2<sup>3<\/sup>\u00d75<sup>3<\/sup>=(2\u00d75)<sup>3<\/sup>=10<sup>3<\/sup>=1000<\/p>\n\n\n\n<p>\u2705 Only works if the <strong>exponents are the same<\/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><strong>Special case \u2013 multiplying powers of 1<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1<sup>n<\/sup>=1 for any n<\/li>\n\n\n\n<li>Example: 1<sup>5<\/sup>\u00d71<sup>3<\/sup>=1<sup>5+3<\/sup>=1<sup>8<\/sup>=1<\/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><strong>Quick tips for students<\/strong> \u270f\ufe0f<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Always check if the <strong>base is the same<\/strong> before adding exponents.<\/li>\n\n\n\n<li>If <strong>bases are different<\/strong>, keep them separate unless the <strong>exponent is the same<\/strong>.<\/li>\n\n\n\n<li>Practice with numbers and variables: x<sup>2<\/sup>\u00d7x<sup>5<\/sup>=x<sup>7<\/sup><\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udca1 <strong>Remember:<\/strong> Multiplication with exponents is about <strong>adding exponents for the same base<\/strong> and <strong>keeping exponents separate for different bases<\/strong>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/h2>\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-f12f99ff281a86c5b0d917f15ee1534e\" style=\"background-color:#7ad2fb\"><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-7e934dd3158f7ebf2fa9063c418c3667\" 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 using positive&nbsp;exponents.<\/strong><\/p>\n\n\n\n<p>a<sup>3<\/sup> .a<sup>3<\/sup> =____.<\/p>\n<\/div><\/div>\n\n\n\n<p>Simplify.<\/p>\n\n\n\n<p>a<sup>3<\/sup> .a<sup>3<\/sup> = a<sup>3+3<\/sup> [<em>Multiply,&nbsp;remembering to add the&nbsp;exponents<\/em>]<\/p>\n\n\n\n<p class=\"has-large-font-size\">a<sup>6<\/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-e133d91b282c91b52e8fec8232adab47\" style=\"background-color:#f1b2b2\"><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-e1e73c8d4146958eae47a380527564fb\" 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 using positive&nbsp;exponents.<\/strong><\/p>\n\n\n\n<p>a<sup>3<\/sup> . a<sup>5<\/sup> =____.<\/p>\n<\/div><\/div>\n\n\n\n<p>Simplify.<\/p>\n\n\n\n<p>a<sup>3<\/sup> . a<sup>5<\/sup> = a<sup>3+5<\/sup> [<em>Multiply,&nbsp;remembering to add the&nbsp;exponents<\/em>]<\/p>\n\n\n\n<p class=\"has-large-font-size\">a<sup>8<\/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-39350bff5f943851b7740a8b67aff100\" style=\"background-color:#f2a2d8\"><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-a53bf7d159a91e5df223e306de09a051\" 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 using positive&nbsp;exponents.<\/strong><\/p>\n\n\n\n<p>a<sup>2<\/sup> . a<sup>5<\/sup> =____.<\/p>\n<\/div><\/div>\n\n\n\n<p>Simplify.<\/p>\n\n\n\n<p>a<sup>2<\/sup> . a<sup>5<\/sup> = a<sup>2+5<\/sup> [<em>Multiply,&nbsp;remembering to add the&nbsp;exponents<\/em>]<\/p>\n\n\n\n<p class=\"has-large-font-size\">a<sup>7<\/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\"><a href=\"https:\/\/wordwall.net\/play\/78129\/751\/481\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-304.png\" alt=\"\" class=\"wp-image-9610\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-304.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-304-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-304-150x150.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\/552\/793\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-311.png\" alt=\"\" class=\"wp-image-9611\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-311.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-311-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-311-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Multiplication with exponents Design by Delta publications Key Notes : Multiplication with Exponents \ud83d\udcda\u2728 What are exponents? An exponent tells us how many times a number is multiplied by itself. Multiplying numbers with the same base \ud83d\udd17 Rule: When multiplying powers with the same base, add their exponents. am\u00d7an=am+n Example: Multiplying numbers with different bases<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/f-8-multiplication-with-exponents\/\">Continue reading <span class=\"screen-reader-text\">&#8220;F.8 Multiplication 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-104","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\/104","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=104"}],"version-history":[{"count":22,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/104\/revisions"}],"predecessor-version":[{"id":22050,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/104\/revisions\/22050"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=104"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}