Group property for division conversion In a group, based on what property the following is possible
$ (\frac{B}{A})^a = g^{ab - a^2} $
where 
$ A = g^a $
$ B = g^b $
$a \epsilon Z_p$
$b \epsilon Z_p$
$Z_p$ is a cyclic group and $g$ is a generator of the group
with reference to first page of paper https://eprint.iacr.org/2015/267.pdf

$(\frac{B}{A})^a=(g^{b-a})^a=g^{ab-a^2}$
I think the main property here is:
$g^ng^m=g^{n+m}$
$g^n/g^m=g^{n-m}$
$(g^n)^k=g^{nk}$
which is similar to the rules for exponential in real numbers.
