Answer
$\dfrac{mn}{r^2}
$
Work Step by Step
The correct right side of the given incorrect equation, $
\dfrac{m}{r}\cdot\dfrac{n}{r}=\dfrac{mn}{r}
,$ is
\begin{array}{l}\require{cancel}
\dfrac{m(n)}{r(r)}
\\\\=
\dfrac{mn}{r^2}
.\end{array}