federalist vs exponent

federalist and exponent both are nouns.

Word	Noun	Adjective	Verb	Adverb
federalist	Yes	No	No	No
exponent	Yes	No	No	No

As nouns, exponent is a hypernym of federalist; that is, exponent is a word with a broader meaning than federalist:

Other hypernyms of federalist include advocate, advocator, proponent.

federalist (noun)	exponent (noun)
an advocate of federalism	a mathematical notation indicating the number of times a quantity is multiplied by itself
	a person who pleads for a cause or propounds an idea
	someone who expounds and interprets or explains