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. $4^{1 / 64}=-3$

Answer

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Answer

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

Steps

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 $\boxed{4^{-3}=\frac{1}{64}}$.

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. $4^{1 / 64}=-3$

Answer

Popular Problems

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. $4^{1 / 64}=-3$