"In this case, i takes values n, n^{1/k}, (n^{1/k})^{1/k} = n^{1/k2}, n^{1/k3}, …, n^{1/klogk(log(n))}, so there are in total log_{k}(log(n)) iterations and each iteration takes time O(1), so the total time complexity is O(log(log(n)))."

Can someone explain the above statement? How do we calculate that there are log_{k}(log(n)) iterations?