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: 43

Answer

$a^{2}b\sqrt[4] (b^{3})$

Work Step by Step

$\sqrt [4] (a^{8}b^{7})=\sqrt [4] (a^{8}) \times\sqrt[4] (b^{4})\times\sqrt[4] (b^{3})=a^{2}b\sqrt[4] (b^{3})$ We know that $\sqrt [4] (a^{8})=a^{2}$, because $(a^{2})^{4}=a^{2\times4}=a^{8}$. We also know that $\sqrt[4] (b^{4})=b$, because $(b)^{4}=b^{4}$.
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