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: 13



Work Step by Step

We are given the expression $(-2^{-2}y^{-1})^{-3}$. 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. $(-2^{-2}y^{-1})^{-3}=(-1)^{-3}\times(2^{-2})^{-3}\times(y^{-1})^{-3}$ 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). $((-1)^{-3})\times(2^{-2\times-3})\times(y^{-1\times-3})=((-1)^{-3})\times(2^{6})\times(y^{3})=-64y^{3}$
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