\[\left( - a^{5} \right)^{3} \cdot \left( - a^{4} \right)^{7}\ :a^{12} =\]
\[= - a^{15} \cdot \left( - a^{28} \right)\ :a^{12} =\]
\[= a^{15 + 28 - 12} = a^{31}\]