Answer
$\dfrac{2,025}{8r^{4}}$
Work Step by Step
Using the laws of exponents, the given expression, $
\left( \dfrac{3r^5}{5r^{-3}} \right)^{-2}\left(\dfrac{9r^{-1}}{2r^{-5}}\right)^3
,$ simplifies to
\begin{array}{l}\require{cancel}
\left( \dfrac{5r^{-3}}{3r^5} \right)^{2}\left(\dfrac{9r^{-1}}{2r^{-5}}\right)^3
\\\\=
\left( \dfrac{5^2r^{-3(2)}}{3^2r^{5(2)}} \right)\left(\dfrac{9^3r^{-1(3)}}{2^3r^{-5(3)}}\right)
\\\\=
\left( \dfrac{5^2r^{-6}}{3^2r^{10}} \right)\left(\dfrac{9^3r^{-3}}{2^3r^{-15}}\right)
\\\\=
\dfrac{5^29^3r^{-6}r^{-3}}{3^22^3r^{10}r^{-15}}
\\\\=
\dfrac{5^2(3^2)^3r^{-6+(-3)-10-(-15)}}{3^22^3}
\\\\=
\dfrac{5^23^6r^{-6-3-10+15}}{3^22^3}
\\\\=
\dfrac{5^23^{6-2}r^{-4}}{2^3}
\\\\=
\dfrac{5^23^{4}}{2^3r^{4}}
\\\\=
\dfrac{(25)(81)}{8r^{4}}
\\\\=
\dfrac{2,025}{8r^{4}}
.\end{array}