\[\left( \frac{a^{- 7}}{d^{5}} \right)^{- 3} \cdot \left( \frac{a^{4}}{d^{- 7}} \right)^{- 5} =\]
\[= \frac{a^{21}}{d^{- 15}} \cdot \frac{a^{- 20}}{d^{35}} = \frac{a}{d^{20}}.\]