powerfully has 2 distinct synonyms spread across 2 of its 2 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
in a powerful manner
“the federal government replaced the powerfully pro-settler Sir Godfrey Huggins with the even tougher and more determined ex-trade unionist”
in a manner having a powerful influence
“Clytemnestra's ghost crying in the night for vengeance remained most potently in the audience's mind”
Synonyms, antonyms and the broader and narrower relations for powerfully come from Princeton University’s WordNet. Full sources and licences.