\[\frac{\left( 2^{2} \cdot 2^{6} \right)^{5}}{\left( 2 \cdot 2^{8} \right)^{4}} = \frac{\left( 2^{8} \right)^{5}}{\left( 2^{9} \right)^{4}} = \frac{2^{40}}{2^{36}} = 2^{4} = 16.\]