{"id":351,"date":"2022-04-13T09:07:44","date_gmt":"2022-04-13T09:07:44","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=351"},"modified":"2024-10-23T14:38:10","modified_gmt":"2024-10-23T14:38:10","slug":"u-6-multiplication-and-division-with-exponents","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/u-6-multiplication-and-division-with-exponents\/","title":{"rendered":"U.6 Multiplication and 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> Multiplication and division with exponents<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#74008b\"><strong>Key Notes :<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p><strong>Multiplication with Exponents<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Product Rule:<\/strong> When multiplying powers with the same base, add the exponents.\n<ul class=\"wp-block-list\">\n<li>a^m * a^n = a^(m+n)<\/li>\n\n\n\n<li>Example: 2\u00b3 * 2\u2074 = 2^(3+4) = 2\u2077<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Multiplying Powers with Different Bases:<\/strong> If the bases are different, you cannot combine the exponents directly.\n<ul class=\"wp-block-list\">\n<li>Example: 3\u00b2 * 5\u2074 cannot be simplified further.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p><strong>Division with Exponents<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Quotient Rule:<\/strong> When dividing powers with the same base, subtract the exponents.\n<ul class=\"wp-block-list\">\n<li>a^m \/ a^n = a^(m-n)<\/li>\n\n\n\n<li>Example: 4\u2075 \/ 4\u00b2 = 4^(5-2) = 4\u00b3<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Dividing Powers with Different Bases:<\/strong> If the bases are different, you cannot combine the exponents directly.\n<ul class=\"wp-block-list\">\n<li>Example: 6\u00b3 \/ 2\u00b2 cannot be simplified further.<\/li>\n<\/ul>\n<\/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-large-font-size wp-elements-8806f4affd6e2a0395e1d92dbd7fe5c0\" style=\"background-color:#d2e3a2\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-5d756e89b4e75d5aec04c5af3f52841e\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>Simplify.&nbsp;Express your answer using positive&nbsp;exponents.<\/strong><\/p>\n\n\n\n<p>n<sup>7<\/sup> . n<sup>\u20139<\/sup>\/n<sup>8<\/sup> = _______<\/p>\n<\/div><\/div>\n\n\n\n<p>First,&nbsp;simplify the&nbsp;numerator.<\/p>\n\n\n\n<p>n<sub><sup>7  <\/sup><\/sub>. n<sup>-9<\/sup> \/ n<sup>8<\/sup><\/p>\n\n\n\n<p>n<sup>7 + -9 <\/sup> \/ n<sup>8<\/sup>   Multiply,&nbsp;remembering to add the&nbsp;exponents<\/p>\n\n\n\n<p>n<sup>-2<\/sup> \/ n<sup>8 <\/sup><\/p>\n\n\n\n<p> The&nbsp;numerator is simplified. Now, divide the numerator by the&nbsp;denominator.<\/p>\n\n\n\n<p>n<sup>-2 &#8211; 8<\/sup>   Divide,&nbsp;remembering to subtract the&nbsp;exponents<\/p>\n\n\n\n<p>n<sup>-10<\/sup><\/p>\n\n\n\n<p>Finally , express your answer using positive exponents<\/p>\n\n\n\n<p>n<sup>-10<\/sup><\/p>\n\n\n\n<p>1 \/ n<sup>10<\/sup><\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-55857251ad4446ad43a905d0c9450bc4\" style=\"background-color:#d0c4f0\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-123775f853d59a8732128da47f6ae68e\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>Simplify.&nbsp;Express your answer using positive&nbsp;exponents.<\/strong><\/p>\n\n\n\n<p>u<sup>\u20136 <\/sup>. u<sup>\u20138<\/sup> . u<sup>3<\/sup> = _________<\/p>\n<\/div><\/div>\n\n\n\n<p>Simplify.<\/p>\n\n\n\n<p>u<sup>-6<\/sup> . u<sup>-8<\/sup> u<sup>3<\/sup><\/p>\n\n\n\n<p>u<sup>-6 + -8 +3<\/sup>   Multiply,&nbsp;remembering to add the&nbsp;exponents<\/p>\n\n\n\n<p>u<sup>-11<\/sup><\/p>\n\n\n\n<p>Finally , express your answer using positive exponents<\/p>\n\n\n\n<p>u<sup>-11<\/sup><\/p>\n\n\n\n<p>1 \/ u<sup>11<\/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-large-font-size wp-elements-038ecf7c8199f50dd76125aa96f73a49\" style=\"background-color:#93e493\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-74d847efc661dedd3474d3003fa93d5b\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>Simplify.&nbsp;Express your answer using positive&nbsp;exponents.<\/strong><\/p>\n\n\n\n<p>b<sup>6<\/sup>  . b<sup>\u20134<\/sup> \/ b<sup>-9<\/sup> = ______<\/p>\n<\/div><\/div>\n\n\n\n<p>First,&nbsp;simplify the&nbsp;numerator.<\/p>\n\n\n\n<p>b<sup>6 <\/sup>. b<sup>\u20134<\/sup>\/b<sup>\u20139<\/sup><\/p>\n\n\n\n<p>b<sup><strong>6<\/strong>+\u2013<strong>4<\/strong><\/sup>\/b<sup>\u20139  <\/sup>       Multiply,&nbsp;remembering to add the&nbsp;exponents<\/p>\n\n\n\n<p>b<strong><sup>2<\/sup><\/strong>\/b<sup>\u20139<\/sup>          The&nbsp;numerator is simplified. Now, divide the numerator by the&nbsp;denominator.<\/p>\n\n\n\n<p>b<sup><strong>2<\/strong>\u2013 \u2013<strong>9<\/strong><\/sup>          Divide,&nbsp;remembering to subtract the&nbsp;exponents<\/p>\n\n\n\n<p>b<strong><sup>11<\/sup><\/strong> <\/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!<\/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\/79944\/246\/116\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-134.png\" alt=\"\" class=\"wp-image-8103\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-134.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-134-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-134-150x150.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\/79777\/667\/625\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-143.png\" alt=\"\" class=\"wp-image-8104\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-143.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-143-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-143-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Multiplication and division with exponents Key Notes : Multiplication with Exponents Division with Exponents Learn with an example Simplify.&nbsp;Express your answer using positive&nbsp;exponents. n7 . n\u20139\/n8 = _______ First,&nbsp;simplify the&nbsp;numerator. n7 . n-9 \/ n8 n7 + -9 \/ n8 Multiply,&nbsp;remembering to add the&nbsp;exponents n-2 \/ n8 The&nbsp;numerator is simplified. Now, divide the numerator by<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/u-6-multiplication-and-division-with-exponents\/\">Continue reading <span class=\"screen-reader-text\">&#8220;U.6 Multiplication and 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-351","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/351","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=351"}],"version-history":[{"count":17,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/351\/revisions"}],"predecessor-version":[{"id":15654,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/351\/revisions\/15654"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=351"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}