In Exodus 7:7, the author mentions the ages of Moses & Aaron when they spoke to Pharaoh:
And Moses was eighty years old and Aaron eighty-three years old when they spoke to Pharaoh.
Why was it of importance to note this?
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Something we see consistently in The Scripture is God showing His Power, His Authoritative Rule over all things.
One example is Him waited till Sarah was past the age of having a child before she gave birth to Issac.
Now interestingly this mention of Moses's age shows up again in Psalm 90 which Moses wrote, "As for the days of our life, they contain seventy years, Or if due to strength, eighty years, Yet their pride is but labor and sorrow; For soon it is gone and we fly away." Psalm 90:10.
From what is said here one who has lived 80 years is one who has Strength while the average person lives about 70 years. Once again God showing his glory in Deuteronomy 34:7 we read "Although Moses was one hundred and twenty years old when he died, his eye was not dim, nor his vigor abated."
The Idea of showing Moses and Aaron's age was to show these were Men who had Strength. But! Was it strength of their own, or of God Almighty?
The word we find H1369 גְּבוּרָה is strength, might strength might, valour, bravery might, mighty deeds (of God)
Deu 3:24 - ‘O Lord GOD, You have begun to show Your servant Your greatness and Your strong hand; for what god is there in heaven or on earth who can do such works and mighty H1369 acts H1369 as Yours?
1Ch 29:11 - “Yours, O LORD, is the greatness and the power H1369 and the glory and the victory and the majesty, indeed everything that is in the heavens and the earth; Yours is the dominion, O LORD, and You exalt Yourself as head over all.
Jer 10:6 - There is none like You, O LORD; You are great, and great is Your name in might. H1369
Now of course this word is used in context of human might but it is to note that Isaiah 40:29 says "He gives strength to the weary, And to him who lacks might He increases power."
So God is in control of who has Strength and who has Might.
So the reason for acknowledging Moses and Aaron's age was for The Glory of God, to establish that these are Men who are strong in The Lord God Almighty and have come up against this wordly king who fancies himself a god. But we soon read after that there is only One True God who's authority reigns across all things.
Matthew 28:18 "And Jesus came up and spoke to them, saying, "All authority has been given to Me in heaven and on earth."
similar to the first answer, that's how long 'it took' God to prepare M. Ex 2:11--3:18 (But Moses said to God, Who am I that I should go to Pharaoh and that I should bring the children of Israel out of Egypt?)
But when he was approaching forty years of age, it came into his heart to visit his brothers, the sons of Israel. And when he saw one of them being wronged, he defended him, and he avenged him who was being oppressed by striking the Egyptian dead. And he supposed that his brothers understood that God through his hand was giving salvation to them; but they did not understand. And on the following day he appeared to them as they were fighting and tried to reconcile them in peace, saying, Men, you are brothers. Why are you wronging one another? But the one who was wronging his neighbor pushed him away, saying, "Who appointed you a ruler and a judge over us? Do you want to do away with me the same way you did away with the Egyptian yesterday?" And Moses fled at this word and became a sojourner in the land of Midian, where he begot two sons. And when forty years had been fulfilled, an Angel appeared to him in the wilderness of Mount Sinai in the flame of a thornbush fire...I am the God of your fathers, the God of Abraham and Isaac and Jacob.'' And Moses trembled...