c. 1400, pouerful, "mighty, having great strength or power," from power (n.) + -ful. Sense of "capable of exerting great force or power" is from 1580s.
Meaning "of great quality or number" is from 1811; hence the colloquial sense of "exceedingly, extremely" (adv.) is from 1822. Thornton ("American Glossary") notes powerful, along with monstrous, Â as "Much used by common people in the sense of very," and cites curious expressions such as devilish good, monstrous pretty (1799), dreadful polite, cruel pretty, abominable fine (1803), "or when a young lady admires a lap dog for being so vastly small and declares him prodigious handsome" (1799).
This gross perversion is common in several of the Western counties of Pennsylvania, to which region I had supposed it was limited. A gentleman informs me, however that it is not unfrequent in the South, and that he has even heard it yoked with weak, as, A powerful weak man. [Seth T. Hurd, "A Grammatical Corrector; or, Vocabulary of the Common Errors of Speech," 1847]
Related: Powerfully; powerfulness.