mightily vs powerful

mightily is not an adjective while powerful is an adjective.

Word	Noun	Adjective	Verb	Adverb
mightily	No	No	No	Yes
powerful	No	Yes	No	Yes

As adverbs, mightily and powerful are synonyms defined as:

mightily and powerful: (Southern regional intensive) very; to a great degree

Other synonyms of mightily include mighty, right.

mightily (adjective)	powerful (adjective)
	having great power or force or potency or effect
	having great influence
	displaying superhuman strength or power
	(of a person) possessing physical strength and weight; rugged and powerful
	strong enough to knock down or overwhelm

mightily (adverb)	powerful (adverb)
(Southern regional intensive) very; to a great degree	(Southern regional intensive) very; to a great degree
powerfully or vigorously