Anyone know why don't exponents change with addition and subtraction and the opposite with division and multiplication?

I know how to do the equations and everything, but I really want to know WHY.

My thanks goes to anyone who can help!

Edit:

If you don't know what I mean...

I was looking for an explanation on why 2x^2+2x^2 = 4x^2

whereas 2x^2 multiplied by 2x^2 = 4x^4