nope. that's ... not a thing at all, actually. there's no way to simplify a sum of powers.

there's nothing wrong with having that idea in your head--from time to time, we all toss around ideas that turn out to be wrong--but it's very easy to disprove that idea with simple examples.

e.g., 1^2 + 1^3 + 1^4 is actually 3, but your method of figuring would give 1^9 = 1.