show off vs exhibit

show off is not a noun while exhibit is a noun.

Word	Noun	Adjective	Verb	Adverb
show off	No	No	Yes	No
exhibit	Yes	No	Yes	No

As verbs, exhibit is a hypernym of show off; that is, exhibit is a word with a broader meaning than show off:

Other hypernyms of show off include display, expose.

show off (noun)	exhibit (noun)
	something shown to the public
	an object or statement produced before a court of law and referred to while giving evidence

show off (verb)	exhibit (verb)
display proudly; act ostentatiously or pretentiously	walk ostentatiously
	give an exhibition of to an interested audience
	to show, make visible or apparent
	show an attribute, property, knowledge, or skill