booster vs exponent

booster and exponent both are nouns.

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

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

Other hypernyms of booster include advocate, advocator, proponent.

booster (noun)	exponent (noun)
an additional dose that makes sure the first dose was effective	a mathematical notation indicating the number of times a quantity is multiplied by itself
the first stage of a multistage rocket	a person who pleads for a cause or propounds an idea
an amplifier for restoring the strength of a transmitted signal	someone who expounds and interprets or explains
a thief who steals goods that are in a store
someone who is an active supporter and advocate
a person who backs a politician or a team etc.