exuberate vs cheer

exuberate is not a noun while cheer is a noun.

Word	Noun	Adjective	Verb	Adverb
exuberate	No	No	Yes	No
cheer	Yes	No	Yes	No

As verbs, cheer is a hypernym of exuberate; that is, cheer is a word with a broader meaning than exuberate:

Other hypernyms of exuberate include cheer up, chirk up.

exuberate (noun)	cheer (noun)
	the quality of being cheerful and dispelling gloom
	a cry or shout of approval

exuberate (verb)	cheer (verb)
to express great joy	become cheerful
	spur on or encourage especially by cheers and shouts
	show approval or good wishes by shouting
	cause (somebody) to feel happier or more cheerful
	give encouragement to