{"id":355,"date":"2022-04-13T09:08:15","date_gmt":"2022-04-13T09:08:15","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=355"},"modified":"2024-10-23T14:39:46","modified_gmt":"2024-10-23T14:39:46","slug":"u-8-evaluate-expressions-using-properties-of-exponents","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/u-8-evaluate-expressions-using-properties-of-exponents\/","title":{"rendered":"U.8 Evaluate expressions using properties of exponents"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Evaluate expressions using properties of 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>Understanding the Properties of 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<\/ul>\n<\/li>\n\n\n\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<\/ul>\n<\/li>\n\n\n\n<li><strong>Power Rule:<\/strong> When raising a power to another power, multiply the exponents.\n<ul class=\"wp-block-list\">\n<li>(a^m)^n = a^(m*n)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Zero Exponent Rule:<\/strong> Any nonzero number raised to the power of 0 is 1.\n<ul class=\"wp-block-list\">\n<li>a^0 = 1 (where a \u2260 0)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Negative Exponent Rule:<\/strong> A nonzero number raised to a negative exponent is equal to the reciprocal of the number raised to the positive exponent.\n<ul class=\"wp-block-list\">\n<li>a^(-n) = 1\/a^n (where a \u2260 0) \u00a0<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p><strong>Evaluating Expressions<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Identify the properties of exponents that apply.<\/strong><\/li>\n\n\n\n<li><strong>Apply the properties step-by-step to simplify the expression.<\/strong><\/li>\n\n\n\n<li><strong>Calculate the final result.<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Examples:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Simplify:<\/strong> (2\u00b3 * 2\u2074) \/ 2\u2075\n<ul class=\"wp-block-list\">\n<li>Apply the product rule: 2^(3+4) \/ 2\u2075<\/li>\n\n\n\n<li>Apply the quotient rule: 2^(7-5)<\/li>\n\n\n\n<li>Simplify: 2\u00b2 = 4<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Evaluate:<\/strong> (3\u207b\u00b2) * (3\u2075)\n<ul class=\"wp-block-list\">\n<li>Apply the product rule: 3^(-2+5)<\/li>\n\n\n\n<li>Simplify: 3\u00b3 = 27<\/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<\/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-966c1461439f613a643087d2313d8dda\" style=\"background-color:#e1a4a4\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-cf946571b6a6a5a3a4dae834003a675e\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-large-font-size\" style=\"color:#b00012\"><strong>Evaluate. Write your answer as a whole number or as a simplified fraction.<\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size\">5<sup>6 <\/sup> \/ 5<sup>4<\/sup> = ________<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-large-font-size\">First combine powers with the same bases.<\/p>\n\n\n\n<p class=\"has-large-font-size\">5<sup>6<\/sup> \/ 5<sup>4<\/sup>  = 5<sup>6 &#8211; 4<\/sup>   Divide the 5&#8217;s, remembering to subtract the exponents<\/p>\n\n\n\n<p>5<sup>2<\/sup><\/p>\n\n\n\n<p>Now evaluate.<\/p>\n\n\n\n<p>5<sup>2<\/sup> = 25<\/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-21892ed9405daef182037065fe0a856d\" style=\"background-color:#bfcaec\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-814f26bdcc0a9f7b64fae344141b0a6a\"><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>Evaluate. Write your answer as a whole number or as a simplified fraction.<\/strong><\/p>\n\n\n\n<p>12<sup>9  <\/sup>\/ 12<sup>7<\/sup> =________<\/p>\n<\/div><\/div>\n\n\n\n<p>First combine powers with the same bases.<\/p>\n\n\n\n<p>12<sup>9 <\/sup>\/ 12<sup>7<\/sup>  = 12<sup>9 &#8211; 7<\/sup> Divide the 12&#8217;s, remembering to subtract the exponents<\/p>\n\n\n\n<p>                = 12<sup>2 <\/sup><\/p>\n\n\n\n<p>Now evaluate.<\/p>\n\n\n\n<p>12<sup>2 <\/sup> = 144<\/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-a3d6161a7fe8a9abf720913f2251103a\" style=\"background-color:#dcb9e5\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-2c805ba848c803fbbfdb4184a95c33a2\"><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>Evaluate. Write your answer as a whole number or as a simplified fraction.<\/strong><\/p>\n\n\n\n<p>7<sup>8 <\/sup> \/ 7<sup>6<\/sup> =________<\/p>\n<\/div><\/div>\n\n\n\n<p>First combine powers with the same bases.<\/p>\n\n\n\n<p>7<sup>8 <\/sup> \/ 7<sup>6<\/sup>  = 7<sup>8 &#8211; 6<\/sup>    Divide the 7&#8217;s, remembering to subtract the exponents<\/p>\n\n\n\n<p>             = 7<sup>2<\/sup><\/p>\n\n\n\n<p>Now evaluate.<\/p>\n\n\n\n<p> 7<sup>2<\/sup> = 49<\/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\/79946\/040\/505\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-132.png\" alt=\"\" class=\"wp-image-8097\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-132.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-132-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-132-150x150.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\/79802\/321\/349\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-141.png\" alt=\"\" class=\"wp-image-8098\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-141.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-141-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-141-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Evaluate expressions using properties of exponents Key Notes : Understanding the Properties of Exponents Evaluating Expressions Examples: Learn with an example Evaluate. Write your answer as a whole number or as a simplified fraction. 56 \/ 54 = ________ First combine powers with the same bases. 56 \/ 54 = 56 &#8211; 4 Divide the<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/u-8-evaluate-expressions-using-properties-of-exponents\/\">Continue reading <span class=\"screen-reader-text\">&#8220;U.8 Evaluate expressions using properties of 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-355","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/355","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=355"}],"version-history":[{"count":16,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/355\/revisions"}],"predecessor-version":[{"id":15656,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/355\/revisions\/15656"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=355"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}