Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.2 - Rational Exponents - Exercise Set: 104

Answer

$\sqrt[10]{x}$

Work Step by Step

RECALL: (1) $\sqrt[n]{a} = a^{\frac{1}{n}}$ (2) $\sqrt{a} = a^{\frac{1}{2}}$ (3) $(a^m)^n= a^{mn}$ Use rule (2) above to obtain: $=\sqrt[5]{x^{\frac{1}{2}}}$ Use rule (1) above to obtain $=(x^{\frac{1}{2}})^{\frac{1}{5}}$ Use rule (3) above to obtain: $=x^{\frac{1}{2} \cdot \frac{1}{5}} \\=x^{\frac{1}{10}}$ Use rule (1) to obtain: $=\sqrt[10]{x}$
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