Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Section 7.2 - Rational Exponents - Exercise Set: 71

Answer

$x^{-\frac{1}{3}}(5+x)$

Work Step by Step

$5x^{-\frac{1}{3}}+x^{\frac{2}{3}}=x^{-\frac{1}{3}}(5)+x^{-\frac{1}{3}}(x^{\frac{3}{3}})=x^{-\frac{1}{3}}(5+x^{\frac{3}{3}})=x^{-\frac{1}{3}}(5+x)$ In this problem, we make use of the product rule, which holds that $a^{m}\times a^{n}=a^{m+n}$. For example, $x^{-\frac{1}{3}}\times x^{\frac{3}{3}}=x^{(-\frac{1}{3}+\frac{3}{3})}=x^{\frac{2}{3}}$
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