Answer
$\dfrac{r^{17}}{9}$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{(3r)^2r^4}{r^{-2}r^{-3}}(9r^{-3})^{-2}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(3r)^2r^4(9r^{-3})^{-2}}{r^{-2}r^{-3}}
\\\\=
\dfrac{3^2r^2r^4(9)^{-2}r^{-3(-2)}}{r^{-2}r^{-3}}
\\\\=
\dfrac{3^2r^{2+4}(9)^{-2}r^{6}}{r^{-2+(-3)}}
\\\\=
\dfrac{3^2r^{6}r^{6}}{9^{2}r^{-5}}
\\\\=
\dfrac{9r^{6+6-(-5)}}{81}
\\\\=
\dfrac{r^{6+6+5}}{9}
\\\\=
\dfrac{r^{17}}{9}
.\end{array}