\[\left( - \frac{3x^{4}}{y^{7}} \right)^{5}\ :\left( \frac{9x^{6}}{y^{8}} \right)^{3} =\]
\[= - \frac{343x^{20}}{y^{35}}\ :\frac{729x^{18}}{y^{24}} =\]
\[= - \frac{243x^{20}y^{24}}{y^{35} \cdot 729x^{18}} = - \frac{x^{2}}{3y^{11}}.\]