{"id":341,"date":"2022-04-13T09:06:15","date_gmt":"2022-04-13T09:06:15","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=341"},"modified":"2024-10-23T14:31:33","modified_gmt":"2024-10-23T14:31:33","slug":"u-1-exponents-with-integer-bases","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/u-1-exponents-with-integer-bases\/","title":{"rendered":"U.1 Exponents with integer bases"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Exponents with integer bases<\/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 Exponents<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>An exponent is a number that indicates how many times a base is multiplied by itself.\n<ul class=\"wp-block-list\">\n<li>For example, in 2\u00b3, the base is 2 and the exponent is 3. This means 2 * 2 * 2.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>The result of raising a base to an exponent is called a power.<\/li>\n<\/ul>\n\n\n\n<p><strong>Laws of Exponents<\/strong><\/p>\n\n\n\n<ol 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>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: 3\u2075 \/ 3\u00b2 = 3^(5-2) = 3\u00b3<\/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\n\n\n<li>Example: (5\u00b2)\u00b3 = 5^(2*3) = 5\u2076<\/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\n\n\n<li>Example: 7\u2070 = 1<\/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\n\n\n<li>Example: 2^(-3) = 1\/2\u00b3 = 1\/8<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p><strong>Applications of Exponents<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Scientific notation: A way to express very large or very small numbers.<\/li>\n\n\n\n<li>Compound interest: Calculating the growth of money over time.<\/li>\n\n\n\n<li>Population growth and decay: Modeling changes in population size.<\/li>\n\n\n\n<li>Exponential functions: Used in various fields, including biology, economics, and physics.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><\/p>\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-b853f2f4d0d51967333d493e10a2f6c4\" style=\"background-color:#95e9ae\"><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-127e3d95608a824d6f22b41ef4cfad85\"><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>Evaluate.<\/strong><\/p>\n\n\n\n<p>simplify 3<sup>2<\/sup> \u22c5 3<sup>4<\/sup><\/p>\n<\/div><\/div>\n\n\n\n<p>you can use the property of exponents that states <\/p>\n\n\n\n<p>a<sup>m<\/sup> \u22c5 a<sup>n<\/sup> = a<sup>m+n<\/sup><\/p>\n\n\n\n<p>Applying this property:<\/p>\n\n\n\n<p>3<sup>2<\/sup> \u22c5 3<sup>4<\/sup> = 3<sup>2+4 <\/sup>= 3<sup>6<\/sup><\/p>\n\n\n\n<p>If you want to calculate the value of 3<sup>6<\/sup> .<\/p>\n\n\n\n<p>3<sup>6 <\/sup>: 729<\/p>\n\n\n\n<p>Therefore, 3<sup>2<\/sup> \u22c5 3<sup>4<\/sup> : 3<sup>6<\/sup> or 729<\/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-ab2850ded6a1ba1366d8bfa1df0eab5a\" style=\"background-color:#81cfe5\"><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-eadb9efad237209b37a9556032027337\"><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\">Evaluate.<\/p>\n\n\n\n<p>10<sup>2<\/sup>&nbsp;= ____________<\/p>\n<\/div><\/div>\n\n\n\n<p>The base is 10 and the exponent is 2. Use 10 as a factor 2 times.<\/p>\n\n\n\n<p>10<sup>2<\/sup> =10 . 10=100<\/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\/79937\/526\/886\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-139.png\" alt=\"\" class=\"wp-image-8118\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-139.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-139-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-139-150x150.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\/79570\/870\/638\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-148.png\" alt=\"\" class=\"wp-image-8119\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-148.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-148-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-148-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Exponents with integer bases Key Notes : Understanding Exponents Laws of Exponents Applications of Exponents Learn with an example Evaluate. simplify 32 \u22c5 34 you can use the property of exponents that states am \u22c5 an = am+n Applying this property: 32 \u22c5 34 = 32+4 = 36 If you want to calculate the value<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/u-1-exponents-with-integer-bases\/\">Continue reading <span class=\"screen-reader-text\">&#8220;U.1 Exponents with integer bases&#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-341","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/341","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=341"}],"version-history":[{"count":22,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/341\/revisions"}],"predecessor-version":[{"id":15650,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/341\/revisions\/15650"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=341"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}