Is 500 mg of amoxicyline 4 x day for 7 days enough to kill a dental abscess?

Maybe: Abscesses usually need to be drained before they will respond in a predictable fashion to antibiotics. Sometimes Amoxicillin will help the abscess to drain spontaneously, but if not your dentist is the person to see.

Yes and No: Just taking an antibiotic without treating the cause of the dental abscess is often not sufficient. The antibiotic may bring the infection under control but the underlying cause should be addressed and treated or the infection will return.