Question: automatic replacements of exp(x)^n by exp(x*n) ?

sometimes I get intermediate expressions generated from other operations that contain terms such as exp(x)^n in them. As an example, exp(x)^3.  In Mathematica, it automatically replaces these by exp(3*x). But in Maple I need to force this change.

For purposes of Latex only, I like to change these terms to exp(3*x) before converting the whole expression to Latex, as it is looks much better that way.

expr:=exp(x)^3;
Physics:-Latex(expr)

                \left({\rm e}^{x}\right)^{3}

expr:=exp(3*x);
Physics:-Latex(expr)

                {\rm e}^{3 x}

I found that doing simplify(expr,exp)  does the trick. It changes exp(x)^n to exp(n*x). But I am worried about applying this whole simplification command to the whole expression, which can be very large, and do not want to change it all yet.

I just want to change any occurance of exp() there, and nothing more.

I tried using subsindent to do that, but it does not work on terms in denominator

restart;
expr:=exp(x)^3*sin(x)+3/(exp(x)^n);
subsindets(expr,'exp(anything)^anything',f->simplify(f,exp))

I tried

subsindets(expr,'1/exp(anything)^anything',f->simplify(f,exp))

and it did not work.

I am still not good at subsindent. How to make it change all exp(x)^n to exp(n*x) everywhere?