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: 96

Answer

$\sqrt[14]{x^{11}}$

Work Step by Step

RECALL: (i) $\sqrt[n]{a} = a^{\frac{1}{n}}$ (ii) $\sqrt[n]{a^m} = a^{\frac{m}{n}}$ (iii) $(ab)^m = a^mb^m$ (iv) $(a^m)^n=a^{mn}$ (v) $a^m \cdot a^n = a^{m+n}$ Use rules (i) and (ii) above to obtain: $=x^{\frac{2}{7}} \cdot x^{\frac{1}{2}}$ Use rule (v) above to obtain: $=x^{\frac{2}{7}+\frac{1}{2}} \\=x^{\frac{4}{14} + \frac{7}{14}} \\=x^{\frac{11}{14}}$ Use rule (ii) to obtain: $\\=\sqrt[14]{x^{11}}$
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