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: 9

Answer

$\frac{c^{18}}{64a^{12}b^{6}}$

Work Step by Step

We are given the expression $(2a^{2}bc^{-3})^{-6}$. To simplify, 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). $(2a^{2}bc^{-3})^{-6}=(2^{-6})\times(a^{2\times-6})\times(b^{1\times-6})\times(c^{-3\times-6})=$ $(2^{-6})\times(a^{-12})\times(b^{-6})\times(c^{18})=\frac{c^{18}}{2^{6}a^{12}b^{6}}=\frac{c^{18}}{64a^{12}b^{6}}$
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