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\left(\frac{1}{16}\right)^{-3p}=64
Use the rules of exponents and logarithms to solve the equation.
\log(\left(\frac{1}{16}\right)^{-3p})=\log(64)
Take the logarithm of both sides of the equation.
-3p\log(\frac{1}{16})=\log(64)
The logarithm of a number raised to a power is the power times the logarithm of the number.
-3p=\frac{\log(64)}{\log(\frac{1}{16})}
Divide both sides by \log(\frac{1}{16}).
-3p=\log_{\frac{1}{16}}\left(64\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
p=-\frac{\frac{3}{2}}{-3}
Divide both sides by -3.