Answer
$5r^{-8} \left( r^{2}-2 \right)$
Work Step by Step
Factoring the given factor, $
5r^{-8}
,$ then the given expression, $
5r^{-6}-10r^{-8}
,$ is equivalent to
\begin{array}{l}\require{cancel}
5r^{-8} \left( \dfrac{5r^{-6}}{5r^{-8}}-\dfrac{10r^{-8}}{5r^{-8}} \right)
\\\\=
5r^{-8} \left( r^{-6-(-8)}-2r^{-8-(-8)} \right)
\\\\=
5r^{-8} \left( r^{-6+8}-2r^{-8+8} \right)
\\\\=
5r^{-8} \left( r^{2}-2r^{0} \right)
\\\\=
5r^{-8} \left( r^{2}-2(1) \right)
\\\\=
5r^{-8} \left( r^{2}-2 \right)
.\end{array}
