cheer vs exult

cheer is a noun but exult is not a noun.

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

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

Other hyponyms of cheer include exuberate, jubilate, rejoice, triumph, buoy up, lighten, lighten up.

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

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