Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Review: 113

Answer

$\dfrac{3}{7\sqrt[3]{3}}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To rationalize the numerator of the given expression, $ \dfrac{\sqrt[3]{9}}{7} ,$ multiply by an expression equal to $1$ which will make the numerator a perfect power of the index. Then extract the root of the factor that is a perfect power of the index. $\bf{\text{Solution Details:}}$ Multiplying the given expression by an expression equal to $1$ which will make the numerator a perfect power of the index results to \begin{array}{l}\require{cancel} \dfrac{\sqrt[3]{9}}{7}\cdot\dfrac{\sqrt[3]{3}}{\sqrt[3]{3}} \\\\= \dfrac{\sqrt[3]{27}}{7\sqrt[3]{3}} \\\\= \dfrac{\sqrt[3]{(3)^3}}{7\sqrt[3]{3}} \\\\= \dfrac{3}{7\sqrt[3]{3}} .\end{array}
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