Etymology
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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").

exact (v.)

"to force or compel to be paid or yielded," 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.

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Definitions of exact
1
exact (v.)
claim as due or just;
Synonyms: demand
exact (v.)
take as an undesirable consequence of some event or state of affairs;
Synonyms: claim / take
2
exact (adj.)
marked by strict and particular and complete accordance with fact;
hit the exact center of the target
an exact copy
an exact mind
exact (adj.)
(of ideas, images, representations, expressions) characterized by perfect conformity to fact or truth; strictly correct;
Synonyms: accurate / precise
From wordnet.princeton.edu