The Collaborative International Dictionary of English v.0.48:

Exact \Ex*act"\, v. t. [imp. & p. p. Exacted; p. pr. & vb. n.
   Exacting.] [From L. exactus, p. p. of exigere; or fr. LL.
   exactare: cf. OF. exacter. See Exact, a.]
   To demand or require authoritatively or peremptorily, as a
   right; to enforce the payment of, or a yielding of; to compel
   to yield or to furnish; hence, to wrest, as a fee or reward
   when none is due; -- followed by from or of before the one
   subjected to exaction; as, to exact tribute, fees, obedience,
   etc., from or of some one.
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         He said into them, Exact no more than that which is
         appointed you.                           --Luke. iii.
                                                  13.
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         Years of servise past
         From grateful souls exact reward at last --Dryden.
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         My designs
         Exact me in another place.               --Massinger.
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The Collaborative International Dictionary of English v.0.48:

Exact \Ex*act"\, a. [L. exactus precise, accurate, p. p. of
   exigere to drive out, to demand, enforce, finish, determine,
   measure; ex out + agere to drive; cf. F. exact. See Agent,
   Act.]
   1. Precisely agreeing with a standard, a fact, or the truth;
      perfectly conforming; neither exceeding nor falling short
      in any respect; true; correct; precise; as, the clock
      keeps exact time; he paid the exact debt; an exact copy of
      a letter; exact accounts.
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            I took a great pains to make out the exact truth.
                                                  --Jowett
                                                  (Thucyd. )
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   2. Habitually careful to agree with a standard, a rule, or a
      promise; accurate; methodical; punctual; as, a man exact
      in observing an appointment; in my doings I was exact. "I
      see thou art exact of taste." --Milton.
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   3. Precisely or definitely conceived or stated; strict.
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            An exact command,
            Larded with many several sorts of reason. --Shak.
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The Collaborative International Dictionary of English v.0.48:

Exact \Ex*act"\, v. i.
   To practice exaction. [R.]
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         The anemy shall not exact upon him.      --Ps. lxxxix.
                                                  22.
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WordNet (r) 3.0 (2006):

exact
    adj 1: marked by strict and particular and complete accordance
           with fact; "an exact mind"; "an exact copy"; "hit the
           exact center of the target" [ant: inexact]
    2: (of ideas, images, representations, expressions)
       characterized by perfect conformity to fact or truth ;
       strictly correct; "a precise image"; "a precise measurement"
       [syn: accurate, exact, precise]
    v 1: claim as due or just; "The bank demanded payment of the
         loan" [syn: demand, exact]
    2: take as an undesirable consequence of some event or state of
       affairs; "the accident claimed three lives"; "The hard work
       took its toll on her" [syn: claim, take, exact]

Moby Thesaurus II by Grady Ward, 1.0:

183 Moby Thesaurus words for "exact":
   accurate, appreciative, ask, ask for, assess, attentive, badger,
   be hurting for, be indicated, blackmail, brook no denial,
   burden with, call for, careful, challenge, charge, charge for,
   claim, clamor for, close, compel, conscientious, conscionable,
   constant, consummate, correct, critical, cry for, cry out for,
   delicate, demand, demanding, detailed, dictate, differential,
   direct, discriminate, discriminating, discriminative, distinctive,
   distinguishing, enforce, enjoin, even, exacting, exigent, express,
   exquisite, extort, extract, faithful, fasten upon, fastidious,
   faultless, fine, finical, finicking, finicky, force from,
   freight with, full, fussy, gouge, have occasion for, heedful,
   identical, impose, impose on, impose upon, indent, inerrable,
   inerrant, infallible, inflict on, inflict upon, insist on,
   insist upon, issue an ultimatum, lay, lay on, leave no option,
   levy, levy blackmail, literal, make a demand, make dutiable,
   mathematical, methodical, meticulous, micrometrically precise,
   microscopic, minute, narrow, necessitate, need, nice, oblige,
   order, order up, orderly, painstaking, particular, perfect,
   picayune, pinch, pinpoint, place, place an order, precious,
   precise, precisian, precisianistic, precisionist, precisionistic,
   prerequire, pro rata, proper, prorate, pry loose from, punctilious,
   punctual, puristic, put, put down, put in requisition, put on,
   put upon, refined, religious, religiously exact, rend, rend from,
   require, requisition, right, rigid, rigorous, rip, rip from,
   saddle with, scientific, scientifically exact, screw, scrupulous,
   scrutinizing, selective, selfsame, sensitive, set, severe, shake,
   shake down, snatch from, special, specific, square, squeeze,
   stick for, strict, subject to, subtle, tactful, take doing,
   take no denial, task, tax, tear from, thorough, tithe, true,
   undeviating, unerring, very, want, want doing, warn,
   weight down with, wrench, wrench from, wrest, wring, wring from,
   yoke with