Answer
$\dfrac{a^{10}}{3b^{9}c^{2}}$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{9a^6b^{-4}c^7}{27a^{-4}b^5c^9}
$, is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{\cancel{9}a^{6-(-4)}b^{-4-5}c^{7-9}}{\cancel{9}\cdot3}
\\\\=
\dfrac{a^{10}b^{-9}c^{-2}}{3}
\\\\=
\dfrac{a^{10}}{3b^{9}c^{2}}
.\end{array}
