\[a = \frac{3}{5};\ \ b = - 1\frac{2}{3}:\]
\[a^{2}b^{3} = \left( \frac{3}{5} \right)^{2} \cdot \left( - 1\frac{2}{3} \right)^{3} =\]
\[= \left( \frac{3}{5} \right)^{2} \cdot \left( - \frac{5}{3} \right)^{3} = - \frac{3^{2} \cdot 5^{3}}{5^{2} \cdot 3^{3}} =\]
\[= - \frac{5}{3} = 1\frac{2}{3}.\]