\[\frac{\left( 2^{3} \right)^{5} \cdot \left( 2^{- 6} \right)^{2}}{4²} = \frac{2^{15} \cdot 2^{- 12}}{\left( 2^{2} \right)^{2}} = \frac{2^{3}}{2^{4}} = \frac{1}{2}.\]