when adding an x with an exponent and one without an exponent don't you add one to the existing exponent anyway? example x^2 + x= x^3 correc

x^2 + x= x^3  ???

I think you might be getting your laws of exponents confused

Note that (x^2)* (x) = x^3

To see why the first thing isn't true (and it has to hold for all real numbers), let x =2

So

2^2 + 2 = 2^3  ???

4 + 2 = 8   ???

No.....that definitely doesn't look right, does it???

So, in general.....aⁿ + a^m ≠ a^m+n