Algebra: A Combined Approach (4th Edition)

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

Chapter 10 - Section 10.3 - Simplifying Radical Expressions - Exercise Set: 70

Answer

$\dfrac{\sqrt[3]{128x^{3}}}{-3\sqrt[3]{2x}}=-\dfrac{4}{3}\sqrt[3]{x^{2}}$

Work Step by Step

$\dfrac{\sqrt[3]{128x^{3}}}{-3\sqrt[3]{2x}}$ Rewrite this expression as $-\dfrac{1}{3}\sqrt[3]{\dfrac{128x^{3}}{2x}}$ $\dfrac{\sqrt[3]{128x^{3}}}{-3\sqrt[3]{2x}}=-\dfrac{1}{3}\sqrt[3]{\dfrac{128x^{3}}{2x}}=...$ Evaluate the division inside the cubic root and simplify: $...=-\dfrac{1}{3}\sqrt[3]{64x^{2}}=-\dfrac{1}{3}\cdot\sqrt[3]{64}\cdot\sqrt[3]{x^{2}}=-\dfrac{1}{3}\cdot4\cdot\sqrt[3]{x^{2}}=-\dfrac{4}{3}\sqrt[3]{x^{2}}$
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