## Intermediate Algebra for College Students (7th Edition)

Published by Pearson

# Chapter 1 - Section 1.6 - Properties of Integral Exponents - Exercise Set - Page 80: 115

#### Answer

$$\frac{1}{100a^{4}b^{12}c^{8}}$$

#### Work Step by Step

$$(\frac{20a^{-3}b^{4}c^{5}}{2a^{-5}b^{-2}c})^{-2}$$ Recall the power rule: $(a^{m})^{n}=a^{mn}$ Thus, $=(\frac{20a^{-3}b^{4}c^{5}}{2a^{-5}b^{-2}c})^{-2}$ $=(\frac{10a^{-3}b^{4}c^{5}}{a^{-5}b^{-2}c})^{-2}$ $=\frac{10^{-2}a^{-3\cdot-2}b^{4\cdot-2}c^{5\cdot-2}}{a^{-5\cdot-2}b^{-2\cdot-2}c^{-2}}$ $=\frac{10^{-2}a^{6}b^{-8}c^{-10}}{a^{10}b^{4}c^{-2}}$ Recall the negative exponent rule: $a^{−n}=\frac{1}{a^{n}}$ and $\frac{1}{a^{-n}} = a^{n}$ Thus, $=\frac{10^{-2}a^{6}b^{-8}c^{-10}}{a^{10}b^{4}c^{-2}}$ $=\frac{a^{6}b^{-8}c^{-10}}{10^{2}a^{10}b^{4}c^{-2}}$ Recall the quotient rule: $\frac{a^{m}}{a^{n}}=a^{m-n}$ and $\frac{a^{n}}{a^{m}}=\frac{1}{a^{m+n}}$ if $m>n$ $=\frac{a^{6}b^{-8}c^{-10}}{10^{2}a^{10}b^{4}c^{-2}}$ $=\frac{1}{10^{2}a^{10-6}b^{4+8}c^{-2+10}}$ $=\frac{1}{10^{2}a^{4}b^{12}c^{8}}$ $=\frac{1}{100a^{4}b^{12}c^{8}}$

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