Let G be a simple graph and k\in\mathbb{N} . Two important graph operations are: the k -th graph power of G , denoted by G^{k} , where G^{k} is the graph obtained from G by adding an edge between every pair of vertices that have a distance at most k , and the complement graph of G , denoted by \overline{G} . In this paper, we studied the relation between the independence numbers of \overline{G}^{k} and \overline{G^k} .