Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 7 - Exponents and Exponential Functions - 7-5 Rational Exponents and Radicals - Practice and Problem-Solving Exercises - Page 450: 25



Work Step by Step

Apply $\ \ \sqrt[n]{a^{m}}=a^{m/n},$ $(24c)^{2/3}= \sqrt[3]{(24c)^{2}} \qquad$ ... power of a product... $=\sqrt[3]{(24)^{2}(c)^{2}}$ $=\sqrt[3]{(2^{3}\cdot 3)^{2}c^{2}}$ $=\sqrt[3]{(2^{3})^{2}\cdot(3)^{2}c^{2}}$ $=\sqrt[3]{(2^{2})^{3}\cdot(3)^{2}c^{2}}$ $=2^{2}\cdot\sqrt[3]{3^{2}c^{2}}$ = $4\sqrt[3]{9c^{2}}$
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