How Absolute changes power rules?

Question

I have a question about power rules, we have f(m,n) :

$\ a^{(m-n)}= \frac{a^m}{a^n}$

which is separable. What about:

$\ a^{|m-n|}= ?$

Is it separable? I want f(m,n)=f(n,m)

Thanks.