Answer
$\dfrac{b^{10}}{a^{12}}$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{a^{-9}b^6}{a^3b^{-4}}
,$ is equivalent to
\begin{array}{l}\require{cancel}
a^{-9-3}b^{6-(-4)}
\\\\=
a^{-9-3}b^{6+4}
\\\\=
a^{-12}b^{10}
\\\\=
\dfrac{b^{10}}{a^{12}}
.\end{array}