\[\frac{2^{x} \cdot 32}{2^{3}} = 64\]
\[\frac{2^{x} \cdot 2^{5}}{2^{3}} = 2^{6}\]
\[2^{x} \cdot 2^{2} = 2^{6}\]
\[2^{x} = 2^{4}\]
\[x = 4.\]