\[\frac{\left( 3^{3} \cdot 3^{5} \right)^{6}}{\left( 3 \cdot 3^{8} \right)^{5}} = \frac{\left( 3^{8} \right)^{6}}{\left( 3^{9} \right)^{5}} = \frac{3^{48}}{3^{45}} = 3^{3} = 27.\]