\[1\frac{7}{9}a^{7}b^{2} \cdot \left( \frac{3}{4}a^{2}b \right)^{3} =\]
\[= \frac{16}{9}a^{7}b² \cdot \frac{27}{64}a^{6}b³ = \frac{3}{4}a^{13}b^{5}\]