\[{3,6}^{- 1} \cdot \left( \frac{1}{6} \right)^{- 2} - 6^{0} =\]
\[= \left( \frac{18}{5} \right)^{- 1} \cdot 6^{2} - 1 = \frac{5}{18} \cdot 36 - 1 =\]
\[= 10 - 1 = 9.\]