{"id":22134,"date":"2025-06-16T13:37:51","date_gmt":"2025-06-16T13:37:51","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=22134"},"modified":"2025-06-16T13:37:52","modified_gmt":"2025-06-16T13:37:52","slug":"which-of-the-following-is-equivalent-to-163-21-2","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/which-of-the-following-is-equivalent-to-163-21-2\/","title":{"rendered":"Which of the following is equivalent to (16^(3\/2))^(1\/2)"},"content":{"rendered":"\n

Which of the following is equivalent to (16^(3\/2))^(1\/2)?<\/p>\n\n\n\n

The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n

Correct Answer:<\/strong> (163\/2)1\/2=163\/4(16^{3\/2})^{1\/2} = 16^{3\/4}<\/p>\n\n\n\n

\n\n\n\n

Step-by-Step Explanation:<\/strong><\/h3>\n\n\n\n

We are given the expression: (163\/2)1\/2(16^{3\/2})^{1\/2}<\/p>\n\n\n\n

This is a power of a power<\/strong> situation. In such expressions, you multiply the exponents<\/strong>: (163\/2)1\/2=16(3\/2)\u22c5(1\/2)=163\/4(16^{3\/2})^{1\/2} = 16^{(3\/2) \\cdot (1\/2)} = 16^{3\/4}<\/p>\n\n\n\n

So, the expression simplifies to: 163\/4\\boxed{16^{3\/4}}<\/p>\n\n\n\n

\n\n\n\n

Understanding the Expression:<\/strong><\/h3>\n\n\n\n

To understand what this means numerically:<\/p>\n\n\n\n

    \n
  • Start with the base<\/strong>, which is 16<\/strong>.<\/li>\n\n\n\n
  • The exponent 3\/4<\/strong> means we:\n
      \n
    • First take the fourth root<\/strong> of 16 (because of the denominator 4),<\/li>\n\n\n\n
    • Then raise the result to the third power<\/strong> (because of the numerator 3).<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n

      Step-by-step:<\/p>\n\n\n\n

        \n
      1. 164=2\\sqrt[4]{16} = 2, because 24=162^4 = 16<\/li>\n\n\n\n
      2. 23=82^3 = 8<\/li>\n<\/ol>\n\n\n\n

        Therefore, the expression evaluates to: (163\/2)1\/2=163\/4=8(16^{3\/2})^{1\/2} = 16^{3\/4} = 8<\/p>\n\n\n\n

        \n\n\n\n

        Why This Is Important in Algebra:<\/strong><\/h3>\n\n\n\n

        Understanding how to manipulate exponents is essential in algebra, especially when dealing with radicals and exponential functions. The key rules used here include:<\/p>\n\n\n\n

          \n
        1. Power of a Power Rule<\/strong>: (am)n=amn(a^m)^n = a^{mn}<\/li>\n\n\n\n
        2. Roots and Fractional Exponents<\/strong>: a1\/n=ana^{1\/n} = \\sqrt[n]{a}<\/li>\n<\/ol>\n\n\n\n

          These rules allow you to simplify complex expressions and solve exponential equations more easily. In science, engineering, and real-world problem-solving, knowing how to handle exponents quickly and correctly is very useful.<\/p>\n\n\n\n

          Thus, the expression (163\/2)1\/2(16^{3\/2})^{1\/2} is equivalent to<\/strong> 163\/4\\boxed{16^{3\/4}}.<\/p>\n","protected":false},"excerpt":{"rendered":"

          Which of the following is equivalent to (16^(3\/2))^(1\/2)? The correct answer and explanation is: Correct Answer: (163\/2)1\/2=163\/4(16^{3\/2})^{1\/2} = 16^{3\/4} Step-by-Step Explanation: We are given the expression: (163\/2)1\/2(16^{3\/2})^{1\/2} This is a power of a power situation. In such expressions, you multiply the exponents: (163\/2)1\/2=16(3\/2)\u22c5(1\/2)=163\/4(16^{3\/2})^{1\/2} = 16^{(3\/2) \\cdot (1\/2)} = 16^{3\/4} So, the expression simplifies to: 163\/4\\boxed{16^{3\/4}} […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-22134","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/22134","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=22134"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/22134\/revisions"}],"predecessor-version":[{"id":22135,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/22134\/revisions\/22135"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=22134"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=22134"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=22134"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}