{"id":152008,"date":"2024-10-10T15:51:44","date_gmt":"2024-10-10T15:51:44","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=152008"},"modified":"2024-10-10T15:51:46","modified_gmt":"2024-10-10T15:51:46","slug":"evaluate-the-expression-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/10\/evaluate-the-expression-2\/","title":{"rendered":"Evaluate the expression"},"content":{"rendered":"\n<p>Evaluate the expression. (7 + 3)^0<\/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>The correct answer is: <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-3-color\"><strong>1<\/strong><\/mark><\/p>\n\n\n\n<p>To evaluate the expression ((7 + 3)^0), we first simplify the expression inside the parentheses:<\/p>\n\n\n\n<p>[<br>7 + 3 = 10<br>]<\/p>\n\n\n\n<p>Now, we have:<\/p>\n\n\n\n<p>[<br>(7 + 3)^0 = 10^0<br>]<\/p>\n\n\n\n<p>According to the properties of exponents, any non-zero number raised to the power of zero is equal to 1. This can be expressed as:<\/p>\n\n\n\n<p>[<br>a^0 = 1 \\quad \\text{for any } a \\neq 0<br>]<\/p>\n\n\n\n<p>In our case, since 10 is a non-zero number, we apply this rule:<\/p>\n\n\n\n<p>[<br>10^0 = 1<br>]<\/p>\n\n\n\n<p>Thus, the final answer to the expression ((7 + 3)^0) is:<\/p>\n\n\n\n<p>[<br>\\boxed{1}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation of the Concept<\/h3>\n\n\n\n<p>The rule that any non-zero number raised to the power of zero equals one can be understood through a few mathematical principles.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Exponent Rules<\/strong>: Exponents represent repeated multiplication. For example, (a^3 = a \\times a \\times a). As you decrease the exponent by one, the base remains but you divide by that base. For instance, (a^3\/a^1 = a^{3-1} = a^2). If you continue this process, when you reach (a^1\/a^1), you get (a^0), which simplifies to 1, assuming (a) is not zero.<\/li>\n\n\n\n<li><strong>Patterns in Powers<\/strong>: If we look at the pattern of powers of a number, such as (2), we can observe:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(2^3 = 8)<\/li>\n\n\n\n<li>(2^2 = 4)<\/li>\n\n\n\n<li>(2^1 = 2)<\/li>\n\n\n\n<li>(2^0 = 1)<\/li>\n\n\n\n<li>(2^{-1} = \\frac{1}{2}) Notice how as we decrease the exponent by 1, we keep dividing by 2. Eventually, when we reach (2^0), it must equal 1 to maintain the consistency of the division by 2.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Applications<\/strong>: Understanding this property is essential in algebra and calculus, as it helps simplify expressions and solve equations involving exponents.<\/li>\n<\/ol>\n\n\n\n<p>In conclusion, the evaluation of ((7 + 3)^0) leads us to the answer 1, highlighting the significance of the exponent rule across various mathematical contexts.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Evaluate the expression. (7 + 3)^0 The Correct Answer and Explanation is : The correct answer is: 1 To evaluate the expression ((7 + 3)^0), we first simplify the expression inside the parentheses: [7 + 3 = 10] Now, we have: [(7 + 3)^0 = 10^0] According to the properties of exponents, any non-zero number [&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-152008","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/152008","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=152008"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/152008\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=152008"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=152008"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=152008"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}