Using \textit{E. Bombieri}'s estimates on exponential sums [Am. J. Math. 88, 71--105 (1966; Zbl 0171.41504)], the author shows that for fixed \(k\), the distance between the least residues of \(a^k\bmod p\) and \(a^{-k}\bmod p\), divided by \(p\), as \(a\) runs through \(1,2,\dots, p-1\), behaves like independent random variables on \([0,1]\). This generalizes Part I [cf. J. Number Theory 61, 301--310 (1996; Zbl 0874.11006)].