We study basic aspects of the sums of nonpositive integral powers of monic polynomials of degree one over a finite field. The combinatorics of cancelation in these sums is rather complicated. The focus is basically on the valuations of these sums in the infinite place of  where q is a power of a prime p. We present the concept of integer with inner q carry over of depth j. For exponents of the form  relative prime to p and k relative prime to q, where k presents inner q carry over of depth j, we give a result to find the valuation at the infinite place of  of the sums of powers under study, for any finite field.

finite fields, power sums, zeta function.