I have an exempt employee that works part of a day is the law still that a salary employee is paid for the full day if he or she works part of the day?

Yes, it is still the law that if they work any part of the day they have to be paid for the full day. But neither Arkansas law nor Florida law (you're posting on the Florida board) forbids you from docking part of her vacation or sick pay for the part of the days she does not work.