{"id":168469,"date":"2024-11-17T15:08:38","date_gmt":"2024-11-17T15:08:38","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=168469"},"modified":"2024-11-17T15:08:40","modified_gmt":"2024-11-17T15:08:40","slug":"7-to-the-power-of-4-times-7-to-the-power-of-negative-power-of-4","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/17\/7-to-the-power-of-4-times-7-to-the-power-of-negative-power-of-4\/","title":{"rendered":"7 to the power of 4 times 7 to the power of negative power of 4"},"content":{"rendered":"\n<p>7 to the power of 4 times 7 to the power of negative power of 4<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve the expression ( 7^4 \\times 7^{-4} ), we can use the properties of exponents. Specifically, when multiplying two terms with the same base, we apply the <strong>product of powers rule<\/strong>, which states:<\/p>\n\n\n\n<p>[<br>a^m \\times a^n = a^{m+n}<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( a ) is the base (in this case, 7),<\/li>\n\n\n\n<li>( m ) and ( n ) are the exponents.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Apply the product of powers rule<\/h3>\n\n\n\n<p>Given the expression ( 7^4 \\times 7^{-4} ), we can apply the product of powers rule:<\/p>\n\n\n\n<p>[<br>7^4 \\times 7^{-4} = 7^{4 + (-4)} = 7^{0}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Simplify the exponent<\/h3>\n\n\n\n<p>When any non-zero number is raised to the power of 0, the result is always 1:<\/p>\n\n\n\n<p>[<br>7^0 = 1<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Final Answer<\/h3>\n\n\n\n<p>Thus, the value of ( 7^4 \\times 7^{-4} ) simplifies to:<\/p>\n\n\n\n<p>[<br>\\boxed{1}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation of the Concepts Involved<\/h3>\n\n\n\n<p>The operation relies on understanding the <strong>rules of exponents<\/strong>. Exponents indicate how many times a number (the base) is multiplied by itself. In the case of positive exponents, such as ( 7^4 ), the base is multiplied four times:<\/p>\n\n\n\n<p>[<br>7^4 = 7 \\times 7 \\times 7 \\times 7 = 2401<br>]<\/p>\n\n\n\n<p>However, when dealing with negative exponents, such as ( 7^{-4} ), the base is divided rather than multiplied. The negative exponent tells us to take the reciprocal of the base raised to the positive exponent:<\/p>\n\n\n\n<p>[<br>7^{-4} = \\frac{1}{7^4} = \\frac{1}{2401}<br>]<\/p>\n\n\n\n<p>Thus, multiplying ( 7^4 ) and ( 7^{-4} ) involves multiplying 2401 by its reciprocal, which equals 1:<\/p>\n\n\n\n<p>[<br>2401 \\times \\frac{1}{2401} = 1<br>]<\/p>\n\n\n\n<p>This is why ( 7^4 \\times 7^{-4} = 7^0 = 1 ).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>7 to the power of 4 times 7 to the power of negative power of 4 The Correct Answer and Explanation is: To solve the expression ( 7^4 \\times 7^{-4} ), we can use the properties of exponents. Specifically, when multiplying two terms with the same base, we apply the product of powers rule, which [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-168469","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168469","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=168469"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168469\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=168469"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=168469"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=168469"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}