What is the meaning of "v'Lo b'Yad Chazakah"?
Rashi #1: Pharaoh will not grant you permission to leave, until I show him 1 My strong Hand.
Rashi #2 (citing Targum Onkelos) and Targum Yonasan: It is not because 2 Pharaoh's hand is strong, that he will not let you go out ( - for it is not strong!)
Seforno and Ramban: Pharaoh will not let you go out, even when I show him My strong Hand. 3
Gur Aryeh: Although it would be clearer for Rashi to state, '... until I take them out with a mighty hand,' the verse does not indicate this. "V'Lo b'Yad Chazakah" means, '[Pharaoh shall not allow you to go,] so long as My 'mighty hand' does not accompany [that exodus].'
Targum Yonasan: But rather, because I intend to chastise him with harsh plagues. Gur Aryeh - According to this explanation (that this verse connects with the following one), the reason that Pharaoh will not initially send out Bnei Yisrael, is so that Hashem should then smite the Egyptians with his wonderous plagues. (See Mizrachi, and what Gur Aryeh responds.)
Seforno: Because I will harden his heart to the point that he will not be afraid, to enable Me to strike him again, as we find in the next Pasuk, "Until I stretch out My Hand and smite Egypt, with all My wonders that I will perform in their midst" (3:20). (See also Ba'al ha'Turim.) Ramban - 'With a strong Hand and an outstretched arm, with great awesomeness, with signs and with wonders;' only then will he permit you to leave.
Why did Hashem find it necessary to wait for Pharaoh to send Yisrael away? Why did He not just take them out?
Oznayim la'Torah #1: To deprive the angel of Egypt of the opportunity of be able to ask why He took Yisrael out of Egypt before the prescribed time. 1
Oznayim la'Torah #2: In order to fulfil the promise that He made to Avraham, "v'Gam Es ha'Goy Asher Ya'avodu, Dan Anochi!" (Bereishis 15:14). 2
Oznayim la'Torah #3: Because following the ten plagues, out of fear that they would all die, 3 the Egyptians willingly lent (or gave) them all their silver and golden vessels and garments, thereby fulfilling the second promise that Hashem made to Avraham - "v'Acharei Chen, Yetze'u bi'Rechush Gadol!" (ibid).