SOLUTION: Find the units digit for 7^197 without using a calculator. Explain how you found your answer. I am completely confused with this! I tried doing 7^1 to get 7, then 7^2 but the

Question 387076: Find the units digit for 7^197 without using a calculator. Explain how you found your answer.
I am completely confused with this!
I tried doing 7^1 to get 7, then 7^2 but there isnt a pattern....
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Find the units digit for 7^197 without using a calculator.
:
Without using a calc you can find that the last digit is repeated every 4 power raises
7^1 = 7
7^2 = 9; last digit when you multiply previous last digit 7*7 = 9
7^3 = 3; last digit when you multiply previous last digit 7*9 = 3
7^4 = 1; last digit when you multiply previous last digit 7*3 = 1
7^5 = 7; " " " " " " " 7*1 = 7
7^6 = 9; " " " " " " " 7*7 = 9
7^7 = 3; " " " " " " " 7*9 = 3
7^8 = 1; " " " " " " " 7*3 = 1
7^9 = 7; " " " " " " " 7*1 = 7
7^10= 9; " " " " " " " 7*7 = 9
:
Can you see the pattern here? repeats after every 4th power
:
Using long diviion, find the remainder 197/4; that would be 1
Therefore the last digit should be 7

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