exercise vs strengthen

exercise is a noun but strengthen is not a noun.

Word	Noun	Adjective	Verb	Adverb
exercise	Yes	No	Yes	No
strengthen	No	No	Yes	No

As verbs, strengthen is a hyponym of exercise; that is, strengthen is a word with a more specific, narrower meaning than exercise:

Other hyponyms of exercise include limber up, loosen up, warm up, train, tumble, tone, tone up, press, weight-lift, weightlift.

exercise (noun)	strengthen (noun)
the activity of exerting your muscles in various ways to keep fit
a task performed or problem solved in order to develop skill or understanding
systematic training by multiple repetitions
the act of using
an action, often used negatively and without consequences
(usually plural) a ceremony that involves processions and speeches

exercise (verb)	strengthen (verb)
do physical exercise	give a healthy elasticity to
give a workout to	gain strength
learn by repetition	make strong or stronger
put to use
carry out or practice; as of jobs and professions