Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - Review Exercises: Chapter 10 - Page 693: 31



Work Step by Step

Extracting the factors that are perfect powers of the index, the given expression simplifies to \begin{array}{l}\require{cancel} \sqrt[4]{\dfrac{48a^{11}}{c^8}} \\\\= \sqrt[4]{\dfrac{16a^{8}}{c^8}\cdot3a^3} \\\\= \sqrt[4]{\left( \dfrac{2a^{2}}{c^2}\right)^4\cdot3a^3} \\\\= \dfrac{2a^{2}}{c^2}\sqrt[4]{3a^3} \\\\= \dfrac{2a^{2}\sqrt[4]{3a^3}}{c^2} .\end{array} Note that all variables are assumed to represent positive numbers.
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