Only if it is in fraction form...p^20 / p^-8 = p^12...you can subtract exponents to get 12.
But, p^20 + p^-8 does not equal p^12...Suppose p = 2...try it out with the calculator.
As a general rule, make sure the exponents are the same: x^3 + x^3 = 2x^3, but you cannot apply this to x^3 + x^5.