Question 1150795
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Look at the pattern in the final digits of 7^n for increasing powers n.  Since we are only interested in the final digit, we only need to keep the last digit after each multiplication.<br><pre>
  7^1 final digit 7
  7^2 final digit 9  (7*7 = 49)
  7^3 final digit 3  (9*7 = 63)
  7^4 final digit 1  (3*7 = 21)
  7^5 final digit 7  (1*7 = 7)
  ...<br></pre>
It should be clear that the sequence of final digits repeats ever 4 powers.<br>
Since the power 72 is a multiple of 4, the final digit of 7^72 is the same as the final digit of 7^4, which is 1.<br>