If $64^5 = 32^x$, what is the value of $2^{-x}$?  Express your answer as a common fraction.
I notice that both $64$ and $32$ are powers of $2$, so I can rewrite the equation using exponents of $2$. I have $64^5 = (2^6)^5 = 2^{30}$ and $32^x = (2^5)^x = 2^{5x}$. Now I can equate the exponents of $2$ on both sides of the equation and get $30 = 5x$. Solving for $x$, I divide both sides by $5$ and get $x = 6$. Now I can plug in $x = 6$ into $2^{-x}$ and get $2^{-6}$. This is the same as $\frac{1}{2^6}$, which is $\frac{1}{64}$. 