Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 5 - Section 5.7 - Negative Exponents and Scientific Notation - Exercise Set: 54

Answer

$\dfrac{1}{x^{12}}$

Work Step by Step

Using the laws of exponents, the given expression, $ \left( \dfrac{x^6}{x^2} \right)^{-3} ,$ simplifies to \begin{array}{l}\require{cancel} \left( x^{6-2} \right)^{-3} \\\\= \left( x^{4} \right)^{-3} \\\\= x^{4(-3)} \\\\= x^{-12} \\\\= \dfrac{1}{x^{12}} .\end{array}
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