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 - Review Exercises - Page 100: 101


$$(5x^{2}y^{-4})^{-3} = \frac{ y^{12}}{125x^{6}}$$

Work Step by Step

$$(5x^{2}y^{-4})^{-3}$$ Recall the product-to-power rule: $(ab)^n$ =$a^{m}b^{n}$ and power rule: $(a^{m})^{n}=a^{mn}$ Thus, $$(5x^{2}y^{-4})^{-3}$$ $$5^{-3}x^{2(-3)}y^{-4(-3)}$$ $$5^{-3}x^{-6}y^{12}$$ Recall the negative exponent rule: $a^{−n}=\frac{1}{a^{n}}$ and $\frac{1}{a^{-n}} = a^{n}$ Thus, $$5^{-3}x^{-6}y^{12}$$ $$\frac{ y^{12}}{5^{3}x^{6}}$$ $$\frac{ y^{12}}{125x^{6}}$$
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