Answer
$\dfrac{1}{4}$
Work Step by Step
RECALL:
(1) $a^{-m} = \dfrac{1}{a^m}$
(2) $a^{mn}= (a^m)^n$
Note that $2x=-x(-2)$
Thus,
$3^{2x} = 3^{-x(-2)}$
Use rule (2) above to obtain:
$3^{-x(-2)} = (3^{-x})^{-2}$
With $3^{-x} = 2$, the expression above is equivalent to:
$(3^{-x})^{-2} = 2^{-2}$
Use rule (1) above to obtain:
$2^{-2} = \dfrac{1}{2^2} = \dfrac{1}{4}$
Thus,
$3^{2x} = \dfrac{1}{4}$
