Intermediate Algebra (6th Edition)

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

Chapter 9 - Cumulative Review: 21a

Answer

$\sqrt[4] (x^{3})$

Work Step by Step

$\sqrt x\times\sqrt[4] x=x^{\frac{1}{2}}\times x^{\frac{1}{4}}$ We can use the product rule to simplify, which holds that $a^{m}\times a^{n}=a^{m+n}$ (where a is a real number, and m and n are positive integers). Therefore, $x^{\frac{1}{2}}\times x^{\frac{1}{4}}=x^{\frac{2}{4}+\frac{1}{4}}=x^{\frac{3}{4}}=\sqrt[4] (x^{3})$
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