Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Section 7.3 - Simplifying Radical Expressions - Exercise Set - Page 433: 58



Work Step by Step

$\sqrt [3](8a^{6}b^{9})=\sqrt[3] (8\times a^{6} \times b^{9})=\sqrt[3] 8\times \sqrt[3] (a^{6})\times \sqrt [3](b^{9})=2a^{2}b^{3}$ We know that $\sqrt[3] 8=2$, because $2^{3}=8$. We also know that $\sqrt[3] (a^{6})=a^{2}$, because $(a^{2})^{3}=a^{2\times3}=a^{6}$ and that $\sqrt[3] (b^{9})=b^{3}$, because $(b^{3})^{3}=b^{3\times3}=b^{9}$.
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