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 - Page 460: 106


$x^{3}\sqrt[3] x^{2}$

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, $\sqrt[12] x^{44}=x^{\frac{44}{12}}=x^{\frac{11}{3}}=\sqrt[3] x^{11}$. $\sqrt[3] x^{11}=\sqrt[3] (x^{9}\times x^{2})=\sqrt[3] x^{9}\times\sqrt[3] x^{2}=x^{3}\sqrt[3] x^{2}$
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