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 - Test - Page 102: 36



Work Step by Step

$$(4x^{-5}y^{2})^{-3}$$ Recall the power rule: $(a^{m})^{n}=a^{mn}$ Thus, $$(4x^{-5}y^{2})^{-3}$$ $$=4^{-3}x^{-5(-3)}y^{2(-3)}$$ $$=4^{-3}x^{15}y^{-6}$$ Recall the negative exponent rule: $a^{−n}=\frac{1}{a^{n}}$ and $\frac{1}{a^{-n}} = a^{n}$ Thus, $$=4^{-3}x^{15}y^{-6}$$ $$=\frac{x^{15}}{4^{3}y^{6}}$$ $$=\frac{x^{15}}{4^{3}y^{6}}$$ $$=\frac{x^{15}}{64y^{6}}$$
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