User blog comment:Deedlit11/Ordinal notations II: Up to the Bachmann-Howard ordinal/@comment-1605058-20130629142358/@comment-5150073-20130629143522

More carefully, (w^m)[n] = (w^(m-1)*w)[n] = w^(m-1)*w[n] = w^(m-1)*n, if we take (a*b)[n] = a*b[n] (a and b are limit ordinals).