Intermediate Algebra (12th Edition)

Published by Pearson

Chapter 7 - Section 7.3 - Simplifying Radicals, the Distance Formula, and Circles - 7.3 Exercises: 88

Answer

$k^4p^{7}\sqrt[]{23k}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given expression, $\sqrt[]{23k^9p^{14}} ,$ find a factor of the radicand that is a perfect power of the index. Then extract the root of that factor. Note that all variables are assumed to represent positive real numbers. $\bf{\text{Solution Details:}}$ Expressing the radicand of the expression above with a factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} \sqrt[]{k^8p^{14}\cdot23k} \\\\= \sqrt[]{(k^4p^{7})^2\cdot23k} \\\\= k^4p^{7}\sqrt[]{23k} .\end{array}

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