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: 83

Answer

$x^2y^3$

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) $(a^m)^n=a^{mn}$ Use the rules above to obtain: $=(x^{10}y^{15})^{\frac{1}{5}} \\=(x^{10})^{\frac{1}{5}}(y^{15})^{\frac{1}{5}} \\=x^{\frac{10}{5}}y^{\frac{15}{5}} \\=x^2y^3$
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