\[\left( x^{3} \cdot x \right)^{3}\ :\ *\ = x^{6}\]
\[\left( x^{3 + 1} \right)^{3}\ :\ *\ = x^{6}\]
\[\left( x^{4} \right)^{3}\ :\ *\ = x^{6}\]
\[x^{12}\ :\ *\ = x^{6}\]
\[*\ = x^{12}\ :x^{6}\]
\[*\ = x^{12 - 6} = x^{6}.\]