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The story of Moses being rescued by Pharaoh's daughter was an immediate grace for Moses as a baby as his life was saved. It was also the perfect set up for the future when God would use Moses to lead Israel out of slavery. Miriam was watching her brother and had the boldness to go to Pharaoh's daughter to ask about someone to nurse the baby. Imagine her mom's surprise when she brings back the baby plus tells her not only is the baby safe, but you will be paid to take care of your own child. She did everything she could to protect the baby and when she could no longer God stepped in and did something amazing. Miriam will be by Moses side as he leads Israel and is an asset to him with her wisdom and boldness (though at times she also was a problem, but what sibling isn't sometimes)
Moses was going to be raised in the household of Pharaoh. This would give him the opportunity for a great education and the ability to learn to read and write. He would likely learn about leadership by being in the home of one of the strongest leaders of that time. God put Moses in a position that would prepare him to be the author of the first 5 books of the Bible, referred to as the Pentateuch. Like Joseph before him, God put Moses in the right place at the right time in the middle of Egyptian power because he had a plan and purpose that would help His people, Israel.