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 - Section 1.6 - Properties of Integral Exponents - Exercise Set - Page 82: 160



Work Step by Step

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