  Let $G$ be a connected Lie group. In this paper, we study the density of the
images of individual power maps $P_k:G\to G:g\mapsto g^k$. We give criteria for
the density of $P_k(G)$ in terms of regular elements, as well as Cartan
subgroups. In fact, we prove that if ${\rm Reg}(G)$ is the set of regular
elements of $G$, then $P_k(G)\cap {\rm Reg}(G)$ is closed in ${\rm Reg}(G)$. On
the other hand, the weak exponentiality of $G$ turns out to be equivalent to
the density of all the power maps $P_k$. In linear Lie groups, weak
exponentiality reduces to the density of $P_2(G)$. We also prove that the
density of the image of $P_k$ for $G$ implies the same for any connected full
rank subgroup.
