Answer
$x=-1$
Work Step by Step
Note that $81=3^4$ so the given equation is equivalent to:
$3^{-2x+2}=3^4$
Using the rule $a^m=a^n\longrightarrow m=n$ gives:
$-2x+2=4$
$-2x=2$
$x=\frac{2}{-2}$
$x=-1$
Check:
$3^{-2*-1+2}=81$
$3^{2+2}=81$
$3^{4}=81$
$81=81$
Thus, the answer is correct.