## Precalculus (6th Edition)

RECALL: (1) $a^{-m} = \dfrac{1}{a^m}$ (2) $\dfrac{a^m}{a^n} = a^{m-n}$ (3) $a^1=a$ Thus: (a) Using rule (1) above gives: $5^{-3}=\dfrac{1}{5^3} = \dfrac{1}{125}$ Thus, the answer is $C$. (b) Using rule (1) above gives: $-5^{-3} = -\dfrac{1}{5^3} = -\dfrac{1}{125}$ Thus, the answer is $D$. (c) Using rule (1) above gives: $(-5)^{-3} = \dfrac{1}{(-5)^3} = \dfrac{1}{-125}=-\dfrac{1}{125}$ Thus, the answer is $D$. (d) Using rule (1) above gives: $-(-5)^{-3} = -\dfrac{1}{(-5)^3}=-\dfrac{1}{-125}=\dfrac{1}{125}$ Thus, the answer is $C$.