Answer
$\dfrac{1}{4}$
Work Step by Step
In order to solve the given problem, we will use the following two rules:
$ (a) a^{-p}=\dfrac{1}{a^p} \\ (b) a^{pq}=(a^p)^q$
We can re-write the expression as: $3^{2x}=(3^{-x})^{-2}$
We will use Rule-(b) as: $3^{-x(-2)}=(3^{-x})^{-2}$
Since, $3^{-x}=2$, then we simplify the expression as: $(3^{-x})^{-2}=2^{-2}$
Now, we will use Rule-(a) as: $2^{-2}=\dfrac{1}{2^2}=\dfrac{1}{4}$
Therefore, $3^{2x}=\dfrac{1}{4}$
