Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 9 - Roots and Radicals - 9.3 - More on Simplifying Radicals - Problem Set 9.3 - Page 412: 16



Work Step by Step

Using the properties of radicals, the given expression, $ \dfrac{\sqrt[3]{16}}{\sqrt[3]{54}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\sqrt[3]{8\cdot2}}{\sqrt[3]{27\cdot2}} \\\\= \dfrac{\sqrt[3]{(2)^3\cdot2}}{\sqrt[3]{(3)^3\cdot2}} \\\\= \dfrac{2\sqrt[3]{2}}{3\sqrt[3]{2}} \\\\= \dfrac{2\cancel{\sqrt[3]{2}}}{3\cancel{\sqrt[3]{2}}} \\\\= \dfrac{2}{3} .\end{array}
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