Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 7 - Section 7.3 - Simplifying Radicals, the Distance Formula, and Circles - 7.3 Exercises: 105


$x^{2}\sqrt x$

Work Step by Step

We know from the radical form of $a^{\frac{m}{n}}$ that $a^{\frac{m}{n}}=\sqrt[n] a^{m}$ (where the indicated roots are real numbers). Therefore, $\sqrt[10] x^{25}=x^{\frac{25}{10}}=x^{\frac{5}{2}}=\sqrt x^{5}$. $\sqrt x^{5}=\sqrt (x^{4}\times x)=x^{2}\sqrt x$
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