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: 14

Answer

$4^{24}y^{24}$

Work Step by Step

We are given the expression $(-4^{-6}y^{-6})^{-4}$. To simplify, we can use the power of a product rule, which holds that $(ab)^{m}=a^{m}b^{m}$ (where a and b are real numbers, and m is an integer). Recall that the negative sign should be treated as a separate term. $(-4^{-6}y^{-6})^{-4}=(-1)^{-4}\times(4^{-6})^{-4}\times(y^{-6})^{-4}$ Next, we can use the power rule, which holds that $(a^{m})^{n}=a^{m\times n}$ (where a is a real number, and m and n are integers). $((-1)^{-4})\times(4^{-6\times-4})\times(y^{-6\times-4})=((-1)^{-4})\times(4^{24})\times(y^{24})=1\times4^{24}\times y^{24}=4^{24}y^{24}$
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