Algebra: A Combined Approach (4th Edition)

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

Chapter 10 - Section 10.4 - Adding, Subtracting, and Multiplying Radical Expressions - Exercise Set: 43

Answer

$-\dfrac{\sqrt[3]{2x^{4}}}{9}+\sqrt[3]{\dfrac{250x^{4}}{27}}=\dfrac{14x\sqrt[3]{2x}}{9}$

Work Step by Step

$-\dfrac{\sqrt[3]{2x^{4}}}{9}+\sqrt[3]{\dfrac{250x^{4}}{27}}$ Rewrite this expression as $\dfrac{\sqrt[3]{125\cdot2x^{4}}}{\sqrt[3]{27}}-\dfrac{\sqrt[3]{2x^{4}}}{9}$ and simplify both terms: $-\dfrac{\sqrt[3]{2x^{4}}}{9}+\sqrt[3]{\dfrac{250x^{4}}{27}}=\dfrac{\sqrt[3]{125\cdot2x^{4}}}{\sqrt[3]{27}}-\dfrac{\sqrt[3]{2x^{4}}}{9}=...$ $...=\dfrac{5x\sqrt[3]{2x}}{3}-\dfrac{x\sqrt[3]{2x}}{9}=...$ Evaluate the substraction and simplify if possible: $...=\Big[\dfrac{5x(3)-x}{9}\Big]\sqrt[3]{2x}=\dfrac{15x-x}{9}\sqrt[3]{2x}=\dfrac{14x\sqrt[3]{2x}}{9}$
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