c. 1400, exempten, "to relieve, to free or permit to be free" (from some requirement or condition, usually undesirable), from Anglo-French exempter, from exempt (adj.); see exempt (adj.). Related: Exempted; exempting.
Old English carleas "free from anxiety; unconcerned," from care (n.) + -less; a compound probably from Proto-Germanic (compare Old Norse kærulauss "quit, free"). Original senses extinct by mid-17c. (now in care-free); main modern meaning "not paying attention, inattentive, not taking due care" is attested by 1560s (in carelessly). Meaning "done or said without care, unconsidered" is from 1650s.