A word u is said to be an n-power prefix of another word w if w?unX*. Let Pi denote the family of words which have i-power prefixes but no (i+1)-power prefix. Words in P1 are called p-primitive words. In this paper, some basic properties of words in sets and Pi are studied. It is shown that the sets Pi, Pi \ Q, Pi∩Q, Q\ Pi, and Pi∪Q for i?1 are disjunctive. That is, they are dense non-regular languages. A characterization of words in for i?2 is derived. Several properties of words in are considered too.
