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The nine signs are: the staff, the hand (both mentioned in 20:17-22), famine, shortage of crops, floods, locusts, lice, frogs, and blood (all mentioned in 7:130-133).
Moses and Aaron had a twofold mission: (1) to Pharaoh and his Court, which failed because of Egyptian arrogance; (2) to the Israelites, for whom the Law was received on Mount Sinai, but they repeatedly rebelled against Allah. In both cases there were miracles ("Clear Signs") and other proofs which showed that they came at Allah's command and were inspired by His authority.