Dense images of the power maps in Lie groups and minimal parabolic subgroups

In this note, we study the density of the images of the k-th power maps P-k : G -> G given by g -> g(k), for a connected Lie group G. We characterize P-k(G) being dense in G in terms of the minimal parabolic subgroups of G. For a simply connected simple Lie group G, we characterize all integers k, for which P-k(G) has dense image in G. We show also that for a simply connected semisimple Lie group weak exponentiality is equivalent to the image of the squaring map being dense.