Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Mid-Chapter Check Point - Page 71: 22

Answer

$2\sqrt[3]{2}$

Work Step by Step

Apply the rule$\quad \displaystyle \frac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\frac{a}{b}}$ $\displaystyle \frac{\sqrt[3]{32}}{\sqrt[3]{2}}=\sqrt[3]{\frac{32}{2}}$ $=\sqrt[3]{16}$ ... recognize a power of 2, $16=2^{4}=2^{3}\cdot 2^{1}$ $=\sqrt[3]{2^{3}\cdot 2^{1}} \quad$... use the rule: $\sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}$ $=\sqrt[3]{2^{3}}\cdot\sqrt[3]{2}\quad $... for odd-indexed roots, $\sqrt[n]{a^{n}}=a$ = $2\sqrt[3]{2}$
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