Intermediate Algebra (6th Edition)

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

Chapter 7 - Review: 38

Answer

$5^{\frac{1}{5}}x^{\frac{2}{5}}y^{\frac{3}{5}}$

Work Step by Step

We are told on page 419 that $\sqrt[n] (a^{m})=a^{\frac{m}{n}}$ (where m and n are positive integers greater than 1 with $\frac{m}{n}$ in simplest form and $\sqrt[n] a$ is a real number). Therefore, $\sqrt[5] (5x^{2}y^{3})=(5x^{2}y^{3})^{\frac{1}{5}}=5^{\frac{1}{5}}x^{\frac{2}{5}}y^{\frac{3}{5}}$
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