Answer
$\dfrac{36}{r^{14}}$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{(3r^2)^2r^{-5}}{r^{-2}r^{3}}(2r^{-6})^{2}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{3^2r^4r^{-5}(2^2r^{-6(2)})}{r^{-2}r^{3}}
\\\\=
\dfrac{9r^4r^{-5}(4r^{-12})}{r^{-2}r^{3}}
\\\\=
36r^{4+(-5)+(-12)-(-2)-3}
\\\\=
36r^{4-5-12+2-3}
\\\\=
36r^{-14}
\\\\=
\dfrac{36}{r^{14}}
.\end{array}