exponent vs doer

exponent and doer both are nouns.

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

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

Other hypernyms of exponent include actor, worker.

exponent (noun)	doer (noun)
a mathematical notation indicating the number of times a quantity is multiplied by itself	a person who acts and gets things done
a person who pleads for a cause or propounds an idea
someone who expounds and interprets or explains