SOLUTION: Find the ones digit of 7 raised to the 7th power raised to the 7th power. I multiplied 7, 14 times and I'm not sure that is correct. Thank you.

Question 170682: Find the ones digit of 7 raised to the 7th power raised to the 7th power. I multiplied 7, 14 times and I'm not sure that is correct. Thank you.
Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
Let's write the equation

Using the power of powers rule, that yields

Now, 7*7 = 49
49*7 = 343
343*7 = 2401
2401 * 7 = 16807
Look at the ones digit above. You can see the pattern 7,9,3,1,7...
So the pattern repeats after each group of 4.
Thus 7^(4x+1) ends in 7
7^(4x+2) ends in 9
7^(4x+3) ends in 3
7^(4x+4) ends in 1
49/4 = 12.25 = (4*12) + 1
That means there are 12 groups of 4, plus one left over. That means you will be left with the ones digit ending in 7
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