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: 107


$\sqrt[6] 432$

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, $\sqrt[3] 4\times\sqrt 3=4^{\frac{1}{3}}\times3^{\frac{1}{2}}=4^{\frac{2}{6}}\times3^{\frac{3}{6}}=\sqrt[6] 4^{2}\times\sqrt[6] 3^{3}=\sqrt[6] (4^{2}\times3^{3})=\sqrt[6] (16\times27)=\sqrt[6] 432$.
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