Which power?

Answer: $9$

Writing it out

$64^6=64\times64\times64\times64\times64\times64$, and $64=16\times4$. So $$\begin{split}64^6&=(16\times4)\times(16\times4)\times(16\times4)\times(16\times4)\times(16\times4)\times(16\times4)\\

&=16\times16\times16\times16\times16\times16\times4\times4\times4\times4\times4\times4\\

&=16\times16\times16\times16\times16\times16\times \hspace{2.9mm}16\hspace{2.9mm} \times \hspace{2.9mm}16\hspace{2.9mm} \times\hspace{2.9mm}16\\

&=16^9\end{split}$$

Using index laws

$64=16\times4$, so $64^6=(16\times4)^6$

                              $=16^6\times4^{2\times3}$

                              $=16^6\times\left(4^2\right)^3$

But $4^2=16$, so $16^6\times\left(4^2\right)^3=16^6\times16^3=16^9$

Writing both numbers in terms of 4

$16=4^2$ and $64=4^3$

So $64^6=\left(4^3\right)^6=4^{3\times6}$

So $64^6=4^{18}=4^{2\times9}=\left(4^2\right)^9=16^9$