Algebra: A Combined Approach (4th Edition)

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

Chapter 10 - Test: 13

Answer

$\frac{2\sqrt[3] {3x^{2}}}{3x}$

Work Step by Step

First, we simplify the expression: $\sqrt[3] \frac{8}{9x}=\frac{\sqrt[3] {2^{3}}}{\sqrt[3] {9x}}=\frac{2}{\sqrt[3] {9x}}$. Now, we multiply the expression by $\sqrt[3] {3x^{2}}$ to rationalize the denominator: =$\frac{2}{\sqrt[3] {9x}}\times\frac{\sqrt[3] {3x^{2}}}{\sqrt[3] {3x^{2}}}$ =$\frac{2\times\sqrt[3] {3x^{2}}}{\sqrt[3] {9x}\times\sqrt[3] {3x^{2}}}$ =$\frac{2\sqrt[3] {3x^{2}}}{\sqrt[3] {9x\times3x^{2}}}$ =$\frac{2\sqrt[3] {3x^{2}}}{\sqrt[3] {27x^{3}}}$ =$\frac{2\sqrt[3] {3x^{2}}}{3x}$
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