\[\frac{\left( a^{- 4} \right)^{3} \cdot a^{6}}{a^{- 5}} = \frac{a^{- 12} \cdot a^{6}}{a^{- 5}} = \frac{a^{- 6}}{a^{- 5}} = a^{- 1} = \frac{1}{a}.\]