exult vs cheer

exult is not a noun while cheer is a noun.

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

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

Other hypernyms of exult include cheer up, chirk up.

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

exult (verb)	cheer (verb)
to express great joy	become cheerful
feel extreme happiness or elation	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