exact

adj

1. 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”

2. 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.”

   “I see thou art exact of taste.”

   “During the whole time of his abode in the university he generally spent thirteen hours of the day in study; by which assiduity besides an exact dispatch of the whole course of philosophy, he read over in a manner all classic authors that are extant[…]”

3. Precisely or definitely conceived or stated; strict.

   “An exact command, Larded with many several sorts of reason.”

4. (not-comparable)Such that the kernel of each morphism is the image of the preceding one.
5. (not-comparable)Such that it preserves short exact sequences.

verb

1. (ambitransitive)To demand and enforce the payment or performance of, sometimes in a forcible or imperious way.

   “to exact tribute, fees, or obedience from someone”

   “He said into them, Exact no more than that which is appointed you.”

   “Their goal is retributive: to exact a price from Palestinian civilians (and in some cases left-wing Israeli Jews, Christians, and Israeli security forces) for actions Israeli authorities take against the settlers, usually building enforcement in illegally built settlements.”

   “She was a superb judge who gave her best and exacted the best from each of us, whether in agreement or disagreement.”

   “[…] a generic, strikingly universal, deity, “ha-elohim,” who tests, who exacts and extracts, and who is the object of fear […]”

2. (transitive)To make desirable or necessary.

   “I vvait, Madam, / To knovv vvhat your commands are; my deſignes / Exact me in another place.”

3. (transitive)To inflict; to forcibly obtain or produce; to visit.

   “to exact revenge on someone”

adv

1. exactly

   “She's wearing the exact same sweater as I am!”