\[\frac{a^{3}b^{2} \cdot \left( a^{2}b \right)^{3}}{a^{5}b^{3}} = \frac{a^{3}b^{2} \cdot a^{6}b^{3}}{a^{5}b^{3}} = \frac{a^{9}b^{5}}{a^{5}b³} = a^{4}b^{2}\ \]