  Let $q$ be a $p$-power where $p$ is a fixed prime. In this paper, we look at
the $p$-power maps on unitriangular group $U(n,q)$ and triangular group
$T(n,q)$. In the spirit of Borel dominance theorem for algebraic groups, we
show that the image of this map contains large size conjugacy classes. For the
triangular group we give a recursive formula to count the image size.
