"A&P" depicts a distinct battle for power. Lengel, the A&P store manager, seems to have the most power in the story. He has the power to publicly humiliate people he thinks don't dress (or act) appropriately. He has the power (or so he claims) to make life hard for Sammy if he quits his job. As we discuss in "What's Up With the Ending?," Lengel probably feels the need to treat the girls this way in order to maintain his position of power in the community. If he didn't say anything, he would be tacitly condoning their behavior and opening the door to more of the same. Sammy and the three girls all seem to lose something from taking a stand against the structures of power that Lengel represents. But is it possible that they gain more than they lose?
The power Lengel exerts is only superficial. He won't be able to stop the times from changing.
Sammy gains power by finally doing something about what he sees as a big problem in his community: too much conformity.