If $3^{2 x}=64$, then $3^{-x}$ is equal to
(A) -32
(B) -8
(C) $\frac{1}{4096}$
(D) $\frac{1}{32}$
(E) $\frac{1}{8}$
Since $3^{2 x}=64$ and $3^{2 x}=\left(3^{x}\right)^{2}$, then $\left(3^{x}\right)^{2}=64$ and so $3^{x}= \pm 8$.

Since $3^{x}>0$, then $3^{x}=8$.

Thus, $3^{-x}=\frac{1}{3^{x}}=\frac{1}{8}$.

ANSWER: (E)