Answer
$\dfrac{1}{49}$
Work Step by Step
RECALL:
(1) $a^{-m} = \dfrac{1}{a^m}$
(2) $a^{mn}= (a^m)^n$
Use rule (1) above to obtain:
$4^{-2x} = \dfrac{1}{4^{2x}}$
Use rule (2) above to obtain:
$\dfrac{1}{4^{2x}} = \dfrac{1}{(4^x)^2}$
Thus,
$4^{-2x} = \dfrac{1}{(4^x)^2}$
With $4^x=7$, the expression above simplifies to:
$=\dfrac{1}{7^2}
\\=\dfrac{1}{49}$