Algebra: A Combined Approach (4th Edition)

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

Chapter 10 - Section 10.5 - Rationalizing Numerators and Denominators of Radical Expressions - Exercise Set: 52

Answer

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

Work Step by Step

$\dfrac{\sqrt[3]{4x}}{\sqrt[3]{z^{4}}}$ First, simplify this expression: $\dfrac{\sqrt[3]{4x}}{\sqrt[3]{z^{4}}}=\dfrac{\sqrt[3]{4x}}{z\sqrt[3]{z}}=...$ Multiply this fraction by $\dfrac{\sqrt[3]{2x^{2}}}{\sqrt[3]{2x^{2}}}$ and simplify again if possible: $...=\dfrac{\sqrt[3]{4x}}{z\sqrt[3]{z}}\cdot\dfrac{\sqrt[3]{2x^{2}}}{\sqrt[3]{2x^{2}}}=\dfrac{\sqrt[3]{8x^{3}}}{z\sqrt[3]{2x^{2}z}}=\dfrac{2x}{z\sqrt[3]{2x^{2}z}}$
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