{"id":257158,"date":"2025-07-16T19:03:56","date_gmt":"2025-07-16T19:03:56","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=257158"},"modified":"2025-07-16T19:03:59","modified_gmt":"2025-07-16T19:03:59","slug":"which-of-the-following-are-equivalent-expressions","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/16\/which-of-the-following-are-equivalent-expressions\/","title":{"rendered":"Which of the following are equivalent expressions"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-487.png\" alt=\"\" class=\"wp-image-257159\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct options are the fourth and fifth expressions:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>5\u00b2(4)\u00b2\u02e3<\/strong><\/li>\n\n\n\n<li><strong>5\u00b2(16\u02e3)<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Here is an explanation of why these expressions are equivalent and the others are not.<\/p>\n\n\n\n<p>To find the equivalent expressions, we need to simplify each option and then compare the results. The key is to apply the rules of exponents, particularly the power of a power rule, which states that (a\u1d50)\u207f = a\u1d50\u207f.<\/p>\n\n\n\n<p>Let&#8217;s examine each expression one by one:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>8(5\u00b2)(4\u02e3):<\/strong>\u00a0We start by simplifying the constant part. 5\u00b2 is 25. Multiplying 8 by 25 gives us 200. So, this expression simplifies to\u00a0<strong>200(4\u02e3)<\/strong>.<\/li>\n\n\n\n<li><strong>400 + 25(4)\u02e3:<\/strong>\u00a0This expression involves addition and cannot be simplified into a single product. It will not be equivalent to the other options that are single terms. For example, if x=1, this expression is 400 + 25(4) = 500, while the first expression is 200(4) = 800.<\/li>\n\n\n\n<li><strong>5(4\u2074 + 4\u02e3):<\/strong>\u00a0Using the distributive property, we get 5(4\u2074) + 5(4\u02e3). Since 4\u2074 = 256, this becomes 5(256) + 5(4\u02e3), which is\u00a0<strong>1280 + 5(4\u02e3)<\/strong>. This is also an expression with two terms and is not equivalent to the others.<\/li>\n\n\n\n<li><strong>5\u00b2(4)\u00b2\u02e3:<\/strong>\u00a0First, 5\u00b2 equals 25. For the exponential part, we can use the power of a power rule. (4)\u00b2\u02e3 is equivalent to (4\u00b2)\u02e3. Since 4\u00b2 is 16, the term becomes 16\u02e3. Combining these parts, the expression simplifies to\u00a0<strong>25(16\u02e3)<\/strong>.<\/li>\n\n\n\n<li><strong>5\u00b2(16\u02e3):<\/strong>\u00a0Here, 5\u00b2 is 25. The expression simplifies directly to\u00a0<strong>25(16\u02e3)<\/strong>.<\/li>\n\n\n\n<li><strong>16(5\u00b2)(4\u02e3):<\/strong>\u00a0The constant part is 16 multiplied by 5\u00b2, which is 16 \u00d7 25 = 400. This expression simplifies to\u00a0<strong>400(4\u02e3)<\/strong>.<\/li>\n<\/ol>\n\n\n\n<p>After simplifying all the options, we can compare them:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Option 1: 200(4\u02e3)<\/li>\n\n\n\n<li>Option 2: 400 + 25(4)\u02e3<\/li>\n\n\n\n<li>Option 3: 1280 + 5(4\u02e3)<\/li>\n\n\n\n<li>Option 4: 25(16\u02e3)<\/li>\n\n\n\n<li>Option 5: 25(16\u02e3)<\/li>\n\n\n\n<li>Option 6: 400(4\u02e3)<\/li>\n<\/ul>\n\n\n\n<p>As you can see, the simplified forms of the fourth and fifth expressions are identical. Therefore,&nbsp;<strong>5\u00b2(4)\u00b2\u02e3<\/strong>&nbsp;and&nbsp;<strong>5\u00b2(16\u02e3)<\/strong>&nbsp;are the only equivalent expressions in the list.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-710.jpeg\" alt=\"\" class=\"wp-image-257160\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: The correct options are the fourth and fifth expressions: Here is an explanation of why these expressions are equivalent and the others are not. To find the equivalent expressions, we need to simplify each option and then compare the results. The key is to apply the rules of exponents, [&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-257158","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/257158","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=257158"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/257158\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=257158"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=257158"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=257158"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}