Answer
$\dfrac{b^{7}}{a^{7}}$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{a^2b^9}{a^9b^2}
,$ simplifies to
\begin{array}{l}\require{cancel}
a^{2-9}b^{9-2}
\\\\=
a^{-7}b^{7}
\\\\=
\dfrac{b^{7}}{a^{7}}
.\end{array}