Write an equivalent expression in exponential form. \[ \log _{4}\left(\frac{1}{64}\right)=-3 \] A. $(-3)^{4}=\frac{1}{64}$ B. $\left(\frac{1}{64}\right)^{-3}=4$ C. $4^{-3}=\frac{1}{64}$ D. $4^{1 / 64}=-3$

Step 1 ：The given logarithmic expression is \(\log _{4}\left(\frac{1}{64}\right)=-3\).

Step 2 ：We can rewrite this in exponential form. The base of the logarithm (4) raised to the power of the result (-3) equals the argument of the logarithm (1/64).

Step 3 ：So, the equivalent expression in exponential form is \(4^{-3}=\frac{1}{64}\).

Step 4 ：Final Answer: The equivalent expression in exponential form is \(\boxed{4^{-3}=\frac{1}{64}}\).