Elementary Algebra

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

Chapter 9 - Roots and Radicals - Chapter 9 Review Problem Set: 53

Answer

$-\sqrt[3]{2}$

Work Step by Step

Using the properties of radicals, the given expression, $ 9\sqrt[3]{2}-5\sqrt[3]{16} ,$ simplifies to \begin{array}{l}\require{cancel} 9\sqrt[3]{2}-5\sqrt[3]{8\cdot2} \\\\= 9\sqrt[3]{2}-5\sqrt[3]{(2)^3\cdot2} \\\\= 9\sqrt[3]{2}-5(2)\sqrt[3]{2} \\\\= 9\sqrt[3]{2}-10\sqrt[3]{2} \\\\= -\sqrt[3]{2} .\end{array}
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