Answer
(a) C
(b) D
(c) D
(d) C
Work Step by Step
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 $C$.
