burn up vs exhaust

burn up is not a noun while exhaust is a noun.

Word	Noun	Adjective	Verb	Adverb
burn up	No	No	Yes	No
exhaust	Yes	No	Yes	No

As verbs, exhaust is a hypernym of burn up; that is, exhaust is a word with a broader meaning than burn up:

Other hypernyms of burn up include consume, deplete, eat, eat up, expend, run through, use, use up, wipe out.

burn up (noun)	exhaust (noun)
	system consisting of the parts of an engine through which burned gases or steam are discharged
	gases ejected from an engine as waste products

burn up (verb)	exhaust (verb)
burn completely; be consumed or destroyed by fire	wear out completely
use up (energy)	eliminate (a substance)
burn brightly	use up the whole supply of
	use up (resources or materials)
	deplete