{"id":146539,"date":"2024-10-01T07:34:33","date_gmt":"2024-10-01T07:34:33","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=146539"},"modified":"2024-10-01T07:34:35","modified_gmt":"2024-10-01T07:34:35","slug":"78%e2%88%924-as-a-fraction-raised-to-a-positive-exponent","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/01\/78%e2%88%924-as-a-fraction-raised-to-a-positive-exponent\/","title":{"rendered":"(78)\u22124 as a fraction raised to a positive exponent"},"content":{"rendered":"\n<p>(78)\u22124 as a fraction raised to a positive exponent.<br>(78)\u22124=<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To express ((78)^{-4}) as a fraction raised to a positive exponent, we can use the properties of exponents. The negative exponent indicates that we take the reciprocal of the base and raise it to the positive of that exponent.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step-by-Step Explanation<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Understanding Negative Exponents<\/strong>: The rule for negative exponents states that (a^{-n} = \\frac{1}{a^n}). This means if we have a negative exponent, we can rewrite the expression as a fraction with the base in the denominator.<\/li>\n\n\n\n<li><strong>Applying the Rule<\/strong>: For our expression ((78)^{-4}), we can apply the negative exponent rule: [<br>(78)^{-4} = \\frac{1}{(78)^4}<br>]<\/li>\n\n\n\n<li><strong>Finding the Positive Exponent<\/strong>: Now that we have rewritten the expression, we see that ((78)^{-4}) is equivalent to (\\frac{1}{(78)^4}). Here, ((78)^4) is a positive exponent because the exponent itself is now positive.<\/li>\n\n\n\n<li><strong>Understanding the Fraction<\/strong>: The expression (\\frac{1}{(78)^4}) represents a fraction where the numerator is 1 and the denominator is (78) raised to the fourth power. This shows that the value of the fraction decreases as the base (78) is raised to a higher exponent.<\/li>\n\n\n\n<li><strong>Calculating the Value (optional)<\/strong>: If we wanted to compute ((78)^4), we could find that: [<br>(78)^4 = 78 \\times 78 \\times 78 \\times 78<br>] However, for our purposes, simply expressing it as a fraction suffices. The specific numeric value isn&#8217;t necessary to understand the exponent transformation.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>Thus, the expression ((78)^{-4}) can be expressed as a fraction with a positive exponent:<\/p>\n\n\n\n<p>[<br>(78)^{-4} = \\frac{1}{(78)^4}<br>]<\/p>\n\n\n\n<p>This demonstrates the fundamental properties of exponents and the simplification process used in algebra to handle negative exponents effectively.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>(78)\u22124 as a fraction raised to a positive exponent.(78)\u22124= The Correct Answer and Explanation is : To express ((78)^{-4}) as a fraction raised to a positive exponent, we can use the properties of exponents. The negative exponent indicates that we take the reciprocal of the base and raise it to the positive of that exponent. [&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-146539","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146539","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=146539"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146539\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=146539"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=146539"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=146539"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}