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 - 10.4 Dividing Radical Expressions - 10.4 Exercise Set: 72

Answer

$\dfrac{2a^2}{\sqrt[3]{28a^2b}}$

Work Step by Step

Rationalizing the numerator, the given expression, $ \sqrt[3]{\dfrac{2a^4}{7b}} ,$ is equivalent to \begin{array}{l} \sqrt[3]{\dfrac{2a^4}{7b}\cdot\dfrac{4a^2}{4a^2}} \\\\= \sqrt[3]{\dfrac{8a^6}{28a^2b}} \\\\= \sqrt[3]{\dfrac{(2a^2)^3}{28a^2b}} \\\\= \dfrac{2a^2}{\sqrt[3]{28a^2b}} .\end{array}
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