For a graph G, its rth power G^r has the same vertex set as G, and has an
edge between any two vertices within distance r of each other in G. We give a
lower bound for the number of edges in the rth power of G in terms of the order
of G and the minimal degree of G. As a corollary we determine how small the
ratio e(G^r)/e(G) can be for regular graphs of diameter at least r