Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 6 - Radical Functions and Rational Exponents - Properties of Exponents - Page 360: 10

Answer

$\dfrac{1}{4x^6y^{14}}$

Work Step by Step

RECALL: (i) $(a^m)^n=a^{mn}$ (ii) $a^{-m} = \dfrac{1}{a^m}, a\ne0$ Use the rules above to have: $=2^{-2}(x^3)^{-2}(y^7)^{-2} \\=\dfrac{1}{2^2} \cdot x^{3(-2)} \cdot y^{7(-2)} \\=\dfrac{1}{4} \cdot x^{-6} \cdot y^{-14} \\=\dfrac{1}{4} \cdot \dfrac{1}{x^6} \cdot \dfrac{1}{y^{14}} \\=\dfrac{1}{4x^6y^{14}}$
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