\[\left( \frac{3a^{4}}{b^{5}} \right)^{- 2} \cdot \left( a^{- 2}b \right)^{- 4} =\]
\[= \left( \frac{b^{5}}{3a^{4}} \right)^{2} \cdot \left( \frac{1}{a^{2}b} \right)^{4} =\]
\[= \frac{b^{10}}{9a^{8} \cdot a^{- 8} \cdot b^{4}} = \frac{b^{6}}{9}\]