\[\left( a^{3} \right)^{2} \cdot \ *\ = - a^{24}\]
\[a^{6} \cdot \ *\ = a^{- 24}\]
\[*\ = \ - a^{24}\ :a^{6}\]
\[*\ = \ - a^{24 - 6}\]
\[*\ = - a^{18}.\]