Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Section 7.3 - Simplifying Radical Expressions - Exercise Set: 70

Answer

$-\dfrac{4\sqrt[3]{x^2}}{3}$

Work Step by Step

Using the properties of radicals, the given expression, $ \dfrac{\sqrt[3]{128x^3}}{-3\sqrt[3]{2x}} ,$ simplifies to \begin{array}{l}\require{cancel} -\dfrac{1}{3}\sqrt[3]{\dfrac{128x^3}{2x}} \\\\= -\dfrac{1}{3}\sqrt[3]{64x^2} \\\\= -\dfrac{1}{3}\sqrt[3]{64\cdot x^2} \\\\= -\dfrac{1}{3}\sqrt[3]{(4)^3\cdot x^2} \\\\= -\dfrac{1}{3}\cdot4\sqrt[3]{x^2} \\\\= -\dfrac{4\sqrt[3]{x^2}}{3} .\end{array}
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