\[\left( \frac{3x}{y^{- 2}} \right)^{- 3} \cdot 81xy = \left( \frac{y^{- 2}}{3x} \right)^{3} \cdot 81xy =\]
\[= \frac{y^{- 6}}{27x^{3}} \cdot 81xy = \frac{3}{x^{2}y^{5}}.\]