Answer
$\frac{b^{7}}{9a^{7}}$
Work Step by Step
We are given the expression $\frac{2a^{-6}b^{2}}{18ab^{-5}}$. We can use the quotient rule to simplify.
$\frac{2a^{-6}b^{2}}{18ab^{-5}}=\frac{2}{18}\times(a^{-6-1})\times(b^{2-(-5)})=\frac{1}{9}a^{-7}b^{7}$
We know that $a^{-n}=\frac{1}{a^{n}}$, so this expression further simplifies to $\frac{b^{7}}{9a^{7}}$.