Answer
Please see the work below.
Work Step by Step
We know that in equilibrium position
$\frac{dU}{dr}=0$
$\implies \frac{-nb}{r^{n+1}}-\frac{-a}{r^2}=0$
This can be rearranged as:
$a-\frac{nb}{r^{n-1}}=0$
$\implies \frac{nb}{r^{n-1}}=a$
$r^{n-1}=\frac{nb}{a}$
$r=\sqrt[n-1] \frac{nb}{a}$
$ r = 2.82 \times 10 ^ {-10} m $
