In this paper, we characterize whether the pure sextic fields Q((6)root m) with square-free integers m not equivalent to +/-1 (mod 9) have power integral bases or do not; if m equivalent to 2, 3 (mod 4), then Q((6)root m) have power integral bases. We prove this by determining relative integral bases of such fields with respect to their cubic and quadratic subfields. Based on the works of Kovacs and Petho, several examples on application of monogenic fields to CNS (Canonical Number System) are shown.