exact (v.)
mid-15c., from Latin exactus, past participle of exigere "require, enforce, demand, collect (money);" see exact (adj.). Older in English than the adjective and retaining the literal sense of the Latin source. Related: Exacted; exacting.
exact (adj.)
"precise, rigorous, accurate," 1530s, from Latin exactus "precise, accurate, highly finished," past participle adjective from exigere "demand, require, enforce," literally "to drive or force out," also "to finish, measure," from ex "out" (see ex-) + agere "to set in motion, drive, drive forward; to do, perform" (from PIE root *ag- "to drive, draw out or forth, move").