postulate vs exact

postulate is a noun but exact is not a noun.

Word	Noun	Adjective	Verb	Adverb
postulate	Yes	No	Yes	No
exact	No	Yes	Yes	No

As verbs, exact is a hyponym of postulate; that is, exact is a word with a more specific, narrower meaning than postulate:

Other hyponyms of postulate include claim, take, govern, draw, cost, cry for, cry out for, compel.

postulate (noun)	exact (noun)
(logic) a proposition that is accepted as true in order to provide a basis for logical reasoning

postulate (adjective)	exact (adjective)
	marked by strict and particular and complete accordance with fact
	(of ideas, images, representations, expressions) characterized by perfect conformity to fact or truth; strictly correct
	lacking compromising or mitigating elements

postulate (verb)	exact (verb)
take as a given; assume as a postulate or axiom	claim as due or just
maintain or assert	take as an undesirable consequence of some event or state of affairs
require as useful, just, or proper