\[\left( - 100a^{3}b^{2} \right)^{4} =\]
\[= ( - 10)^{4} \cdot \left( a^{3} \right)^{4} \cdot \left( b^{2} \right)^{4} =\]
\[= 10\ 000a^{12}b^{8}.\]