Laws of Indices

Are pretty simple.

a^m x aⁿ = a^m+n

a^m / aⁿ = a ^m-n

(a^m)ⁿ = a ^mxn


But a^m + aⁿ DOES NOT equal anything other than what it says.
There isn't much you can do to collect the terms if the indices are different, or if the constant is different (ie x^m + y^m)

a^m + a^m = 2(a^m), of course.