{"id":229025,"date":"2025-06-07T19:54:34","date_gmt":"2025-06-07T19:54:34","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=229025"},"modified":"2025-06-07T19:54:36","modified_gmt":"2025-06-07T19:54:36","slug":"which-expression-is-equivalent-to-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/07\/which-expression-is-equivalent-to-2\/","title":{"rendered":"Which expression is equivalent to"},"content":{"rendered":"\n

Which expression is equivalent to<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Let’s evaluate the expression step-by-step.<\/p>\n\n\n\n

We are given: (454\u22c5414412)12\\left(\\frac{4^{\\frac{5}{4}} \\cdot 4^{\\frac{1}{4}}}{4^{\\frac{1}{2}}}\\right)^{\\frac{1}{2}}(421\u200b445\u200b\u22c5441\u200b\u200b)21\u200b<\/p>\n\n\n\n

Step 1: Simplify the numerator using laws of exponents<\/h3>\n\n\n\n

When multiplying expressions with the same base, add the exponents: 454\u22c5414=454+14=464=4324^{\\frac{5}{4}} \\cdot 4^{\\frac{1}{4}} = 4^{\\frac{5}{4} + \\frac{1}{4}} = 4^{\\frac{6}{4}} = 4^{\\frac{3}{2}}445\u200b\u22c5441\u200b=445\u200b+41\u200b=446\u200b=423\u200b<\/p>\n\n\n\n

So the whole expression becomes: (432412)12\\left(\\frac{4^{\\frac{3}{2}}}{4^{\\frac{1}{2}}}\\right)^{\\frac{1}{2}}(421\u200b423\u200b\u200b)21\u200b<\/p>\n\n\n\n

Step 2: Simplify the fraction<\/h3>\n\n\n\n

When dividing powers with the same base, subtract the exponents: 432412=432\u221212=41\\frac{4^{\\frac{3}{2}}}{4^{\\frac{1}{2}}} = 4^{\\frac{3}{2} – \\frac{1}{2}} = 4^{1}421\u200b423\u200b\u200b=423\u200b\u221221\u200b=41<\/p>\n\n\n\n

Now the expression is: (41)12=412=4=2(4^1)^{\\frac{1}{2}} = 4^{\\frac{1}{2}} = \\sqrt{4} = 2(41)21\u200b=421\u200b=4\u200b=2<\/p>\n\n\n\n

Final Answer:<\/h3>\n\n\n\n

2\\boxed{2}2\u200b<\/p>\n\n\n\n

\n\n\n\n

Explanation<\/strong><\/h3>\n\n\n\n

This problem tests your understanding of the laws of exponents and how to simplify radical and exponential expressions. You’re given a complex expression involving exponents and a radical, and the goal is to simplify it step-by-step using exponent rules.<\/p>\n\n\n\n

We begin with the expression inside the parentheses: 454\u22c5414412\\frac{4^{\\frac{5}{4}} \\cdot 4^{\\frac{1}{4}}}{4^{\\frac{1}{2}}}421\u200b445\u200b\u22c5441\u200b\u200b<\/p>\n\n\n\n

Using the rule for multiplying powers with the same base, we add the exponents: 454+14=464=4324^{\\frac{5}{4} + \\frac{1}{4}} = 4^{\\frac{6}{4}} = 4^{\\frac{3}{2}}445\u200b+41\u200b=446\u200b=423\u200b<\/p>\n\n\n\n

Next, we divide by 4124^{\\frac{1}{2}}421\u200b. Again, applying the law for dividing powers: 432\u00f7412=432\u221212=414^{\\frac{3}{2}} \\div 4^{\\frac{1}{2}} = 4^{\\frac{3}{2} – \\frac{1}{2}} = 4^1423\u200b\u00f7421\u200b=423\u200b\u221221\u200b=41<\/p>\n\n\n\n

Now the entire expression becomes (41)12(4^1)^{\\frac{1}{2}}(41)21\u200b. When you raise a power to a power, you multiply the exponents: (41)12=412=4=2(4^1)^{\\frac{1}{2}} = 4^{\\frac{1}{2}} = \\sqrt{4} = 2(41)21\u200b=421\u200b=4\u200b=2<\/p>\n\n\n\n

Thus, the simplified expression is equal to 2. This shows the power of understanding exponent rules to break down and simplify complex-looking expressions into basic numerical answers.<\/p>\n\n\n\n

Correct answer:<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n","protected":false},"excerpt":{"rendered":"

Which expression is equivalent to The Correct Answer and Explanation is: Let’s evaluate the expression step-by-step. We are given: (454\u22c5414412)12\\left(\\frac{4^{\\frac{5}{4}} \\cdot 4^{\\frac{1}{4}}}{4^{\\frac{1}{2}}}\\right)^{\\frac{1}{2}}(421\u200b445\u200b\u22c5441\u200b\u200b)21\u200b Step 1: Simplify the numerator using laws of exponents When multiplying expressions with the same base, add the exponents: 454\u22c5414=454+14=464=4324^{\\frac{5}{4}} \\cdot 4^{\\frac{1}{4}} = 4^{\\frac{5}{4} + \\frac{1}{4}} = 4^{\\frac{6}{4}} = 4^{\\frac{3}{2}}445\u200b\u22c5441\u200b=445\u200b+41\u200b=446\u200b=423\u200b So the whole […]<\/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-229025","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/229025","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=229025"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/229025\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=229025"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=229025"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=229025"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}