Definition from Wiktionary, the free dictionary
From Old French, from Medieval Latin exactare, reg., from Latin exactus, perfect passive participle of exigō (“demand, claim as due" or "measure by a standard, weigh, test”), from ex (“out”) + agō (“drive”).
- Precisely agreeing with a standard, a fact, or the truth; perfectly conforming; neither exceeding nor falling short in any respect.
- The clock keeps exact time.
- He paid the exact debt.
- an exact copy of a letter
- exact accounts
- Habitually careful to agree with a standard, a rule, or a promise; accurate; methodical; punctual
- a man exact in observing an appointment
- In my doings I was exact.
- Precisely or definitely conceived or stated; strict.
- (algebra, of a sequence of groups connected by homomorphisms) Such that the kernel of one homomorphism is the image of the preceding one.
- (precisely agreeing): perfect, true, correct, precise
- (precisely or definitely conceived or stated): strict
- spot on
- (precisely agreeing): inexact, imprecise, approximate
- (precisely or definitely conceived or stated): loose
Derived terms 
precisely conceived or stated
such that kernel equals image
- (transitive) To demand and enforce the payment or performance of.
- (transitive) To make desirable or necessary.
- (transitive) To forcibly obtain or produce.
- to exact revenge
To make desirable or necessary
Derived terms 
- exact in Webster’s Revised Unabridged Dictionary, G. & C. Merriam, 1913
- exact in The Century Dictionary, The Century Co., New York, 1911
- exact at OneLook Dictionary Search
From French exact.
- exact, precise