how does reputation through 12 angry angry show that power can be abused for personal gain

I don't think it is just power rather than the power of class and race that is at play here. The play proudly presents a tremendous cross-section of American life. The play juxtaposes a presumably wealthy stock broker (4th Juror) with someone who has admittedly lived in the slums his entire life (5th Juror), and we seem to have every level of working man in between. For many of the jurors, we have no more information than their occupation, which gives us an idea of socioeconomic level. These people are defined by what they do for a living. 7th Juror is even so tactless as to report his income of $28000, from selling marmalade, to the group.

Similarly, the idea of class in American society is brought to the forefront in the deliberation. 8th Juror immediately cites the boy's poor upbringing as a possible explanation for his juvenile criminal record and suggests that he has not been given adequate representation, due to his low social status. It calls into immediate question whether the American justice system is fair across classes.

Prejudice is observed on several levels throughout the course of the play. In the most obvious sense, the play deals with racial prejudice. While, conspicuously, the race of the accused is never certain, we do understand that he is a minority of some sort (in the 1957 film, the actor playing the accused was Italian), and this quickly becomes a heated issue among the jurors, especially for 9th Juror, who refers to the accused as "one of them."