\[\left( 11^{- 8} \right)^{7} \cdot \left( 11^{- 9} \right)^{- 6} =\]
\[= 11^{- 56} \cdot 11^{54} = 11^{- 2} =\]
\[= \frac{1}{11^{2}} = \frac{1}{121}.\]