Why don't we change the exponents during like terms?

Answer 1

Exponents are higher in priority in terms of the order of operations, and do not combine in the same way as you would simple add/subtract/multiply/divide.

So, if you have:

26 + 24

This is a polynomial in base 2 with different powers. It would be this in binary:

1010000

...which would not be the same as 210:

1000000000

In order to be able to change exponents, you have to be multiplying factors using the same base, as in:

26 * 24 = 210

...because the exponents are also indicating how many times you are multiplying each base by itself, and multiplication is the same as the basal function of the exponent (repeated multiplication).