College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.6 - Rational Exponents - R.6 Exercises: 65

Answer

$x^{3}y^{8}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the laws of exponents to simplify the given expression, $ \dfrac{(x^{1/4}y^{2/5})^{20}}{x^2} .$ $\bf{\text{Solution Details:}}$ Using the extended Power Rule of the laws of exponents which is given by $\left( x^my^n \right)^p=x^{mp}y^{np},$ the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{x^{\frac{1}{4}\cdot{20}}y^{\frac{2}{5}\cdot{20}}}{x^2} \\\\= \dfrac{x^{5}y^{8}}{x^2} .\end{array} Using the Quotient Rule of the laws of exponents which states that $\dfrac{x^m}{x^n}=x^{m-n},$ the expression above simplifies to \begin{array}{l}\require{cancel} x^{5-2}y^{8} \\\\ x^{3}y^{8} .\end{array}
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