populist vs exponent

populist and exponent both are nouns.

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

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

populist: someone who advocates the rights of the common people over those of the elite
exponent: a person who pleads for a cause or propounds an idea

Other hypernyms of populist include advocate, advocator, proponent.

populist (noun)	exponent (noun)
someone who advocates the rights of the common people over those of the elite	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