Intermediate Algebra (6th Edition)

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

Chapter 5 - Section 5.2 - More Work with Exponents and Scientific Notation - Exercise Set - Page 268: 55

Answer

$\dfrac{2}{x^{4}y^{10}}$

Work Step by Step

Using laws of exponents, the given expression simplifies to \begin{align*} & \left( \dfrac{2x^2}{y^4} \right)^3\left( \dfrac{2x^5}{y} \right)^{-2} \\\\&= \left( \dfrac{2^3x^{2(3)}}{y^{4(3)}} \right)\left( \dfrac{2^{-2}x^{5(-2)}}{y^{-2}} \right) \\\\&= \left( \dfrac{8x^{6}}{y^{12}} \right)\left( \dfrac{x^{-10}}{2^{2}y^{-2}} \right) \\\\&= \dfrac{8x^{6+(-10)}}{4y^{12+(-2)}} \\\\&= \dfrac{2x^{-4}}{y^{10}} \\\\&= \dfrac{2}{x^{4}y^{10}} .\end{align*}
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