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: 12

Answer

$\sqrt[4] (27 a^{2} b^{3})$

Work Step by Step

The product rule holds that $\sqrt[n] a\times\sqrt[n] b=\sqrt[n] (ab)$ (where $\sqrt[n] a$ and $\sqrt[n] b$ are real numbers). Therefore, $\sqrt[4] ab^{2}\times\sqrt[4] 27ab=\sqrt[4] (ab^{2}\times27ab)=\sqrt[4] (27\times a^{1+1}\times b^{2+1})=\sqrt[4] (27 a^{2} b^{3})$
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