For a meromorphic function f, let N ( l + 1 ( r , 1 f ) denote the counting function of zeros of f of order l at least. Let f be a nonconstant meromorphic function, such that . Denote F = f n . Suppose that F and F′ share 1 CM. If (1) n ≥ 3, or N ( r , 1 f ) = O ( N ( 3 ( r , 1 f ) ) , then, F = F′, and f assumes the form f ( z ) = c e 1 n z , where c is a nonzero constant. This main result of this article gives a positive answer to a question raised by Zhang and Yang [1] for the meromorphic functions case in some sense. And a relative result is proved.