In this paper, we have presented a family of fourth order iterative method and another family of sixth order iterative method without memory based on power mean using weight functions. The family of fourth order methods given here is optimal in the sense of Kung-Traub hypothesis. In terms of computational point of view, our rst method require three evaluations (one function and two rst derivatives) per iteration to get fourth order and the second method require four eval- uations (two functions and two derivatives) per iteration to get sixth order. Hence, these methods have high eciency indices 1.5874 and 1.5651 respectively. Few existing methods can be regarded as particu- lar cases of our family of methods. Some numerical examples are tested to know the performance of the new methods which veri es the theo- retical results.