\[\left( \frac{a^{7}}{b^{- 3}} \right)^{- 4} \cdot \left( \frac{a^{- 3}}{b^{9}} \right)^{- 12} =\]
\[= \frac{a^{- 28} \cdot a^{36}}{b^{12} \cdot b^{- 108}} = \frac{a^{8}}{b^{- 96}} = a^{8} \cdot b^{96}\]