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: 51

Answer

$\dfrac{1}{x^{30}b^{6}c^{6}}$

Work Step by Step

Using laws of exponents, the given expression simplifies to \begin{align*} & x^6\left( x^6bc \right)^{-6} \\\\&= x^6\left( x^{6(-6)}b^{-6}c^{-6} \right) \\\\&= x^6\left( x^{-36}b^{-6}c^{-6} \right) \\\\&= x^{6+(-36)}b^{-6}c^{-6} \\\\&= x^{-30}b^{-6}c^{-6} \\\\&= \dfrac{1}{x^{30}b^{6}c^{6}} .\end{align*}
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