The board of regents so constituted shall have power to prescribe such rules, bylaws and regulations as may be proper for the board and for the government of the municipal university, its faculty, instructors, other employees and all students attending the university, subject to the existing laws of the state and of the United States. Said board of regents shall also have power to fix reasonable tuition and other charges to be paid by students attending said university, and may, in its discretion make additional charges to students who are not residents of the taxing district of said university.