With a strong hand - יד חזקה yad chazakah, the same verb which we translate to harden; see Clarke on Exo 4:21 (note). The strong hand here means sovereign power, suddenly and forcibly applied. God purposed to manifest his sovereign power in the sight of Pharaoh and the Egyptians; in consequence of which Pharaoh would manifest his power and authority as sovereign of Egypt, in dismissing and thrusting out the people. See Exo 12:31-33.