Earlier quoted context omitted.
(a^n) * (a^m) = (a*a*a*a*a) * (a*a*a*a*a*a*a) ^ ^ n times m times I don't see what is simpler than this, It comes from the basic definition of what a power is.
this, with the associative law
I could have wrote it without ( ) and I don't think we learn what associative means in highschool.