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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 $P_2(G)$. 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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 $P_2(G)$. 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