Answer
$\dfrac{1}{16x^2}$
Work Step by Step
RECALL:
(1) $a^{-m} = \dfrac{1}{a^m}$
(2) $\dfrac{a^m}{a^n} = a^{m-n}$
(3) $\left(\dfrac{a}{b}\right)^m=\dfrac{a^m}{b^m}$
(4) $(ab)^m = a^mb^m$
Use rule (1) above to obtain:
$(4x)^{-2} = \dfrac{1}{(4x)^2}$
Use rule (4) above to obtain:
$=\dfrac{1}{4^2x^2}
\\=\dfrac{1}{16x^2}$
