Answer
$81a^{2}b^{6}$
Work Step by Step
We simplify this equation by raising each term in the expression to the power of $2$:
$(9ab^{3})^{2}$
=$9^{2}\times a^{2}\times (b^{3})^{2}$
=$81\times a^{2}\times (b^{3\times2})$
=$81\times a^{2}\times (b^{6})$
=$81a^{2}b^{6}$