#### Answer

(a) B
(b) D
(c) B
(d) D

#### 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: $4^{-2}=\dfrac{1}{4^2} = \dfrac{1}{16}$
Thus, the answer is $B$.
(b) Using rule (1) above gives: $-4^{-2} = -\dfrac{1}{4^2} = -\dfrac{1}{16}$
Thus, the answer is $D$.
(c) Using rule (1) above gives: $(-4)^{-2} = \dfrac{1}{(-4)^2} = \dfrac{1}{16}$
Thus, the answer is $B$.
(d) Using rule (1) above gives: $-(-4)^{-2} = -\dfrac{1}{(-4)^2}=-\dfrac{1}{16}$
Thus, the answer is $D$.