Answer
$t = -4$
Work Step by Step
$(\frac{1}{3})^{t} = 81$
$(3^{-1})^{t} = 81$
$3^{-t} = 81$
$3^{-t} = 3^{4}$
$-t = 4$
$t = -4$
Check:
$(\frac{1}{3})^{t} \overset{?}{=} 81$
$(\frac{1}{3})^{-4} \overset{?}{=} 81$
$(3^{-1})^{-4} \overset{?}{=} 81$
$(3)^{4} \overset{?}{=} 81$
$81 = 81$
