Let k be a finite extension of ℚ and L be an extension of k with rings of integers Ok and OL, respectively. If OL=Ok[θ], for some θ in OL, then OL is said to have a power basis over Ok. In this paper, we show that for a Galois extension L/k of degree pm with p prime, if each prime ideal of k above p is ramified in L and does not split in L/k and the intersection of the first ramification groups of all the prime ideals of L above p is non‐trivial, and if p−1 ∤ 2[k:ℚ], then OL does not have a power basis over Ok. Here, k is either an extension with p unramified or a Galois extension of ℚ, so k is quite arbitrary. From this, for such a k the ring of integers of the nth layer of the cyclotomic ℤp‐extension of k does not have a power basis over Ok, if (p, [k:ℚ])=1. Our results generalize those by Payan and Horinouchi, who treated the case k a quadratic number field and L a cyclic extension of k of prime degree. When k=ℚ, we have a little stronger result.