Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 1 - Section 1.6 - Properties of Integral Exponents - Exercise Set - Page 82: 159


$$(x^{-4n} \cdot x^{n})^{-3}= x^{9n}$$

Work Step by Step

$$(x^{-4n} \cdot x^{n})^{-3}$$ Recall the Products to Powers rule: $(ab)^{n} = a^{n}\cdot b^{n}$ Thus, $$(x^{-4n} \cdot x^{n})^{-3}$$ $$=x^{(-4n)(-3)} \cdot x^{(n)(-3)}$$ $$=x^{12n} \cdot x^{-3n}$$ Recall the product rule: $a^{m}⋅a^{n}=a^{m+n}$ Thus, $$x^{12n} \cdot x^{-3n} = x^{9n}$$
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