Green’s Dictionary of Slang

power v.

[SE power, to move with speed or force]

1. (US) to persuade through threats and/or violence.

[US]R. Campbell In La-La Land We Trust (1999) 148: You go around tryin’ to power a strange cunt into doin’ this or that — you grab her by the hair and knock her against the wall — what you got is a bitch yellin’ rape on you.

2. (US campus) to drink beer quickly.

[US] P. Munro Sl. U.

In phrases

power on (v.) (also power through)

(US campus) to do well, to succeed.

[US]P. Munro Sl. U. 151: power on/power through to do well on.