I think there is an easier/faster method for this one...... we have series of 7,9,3,1,7,9,3,1...... sets of 4 numbers (7,9,3,1).....
closest number to 75 which is divisible by 4 is 76.... therefore 7^76 will have 1 at unit place.........
.that means it will be 3 at the 75th power....so 3+6 will give '9' at unit place for the final answer
for example if we want to find out unit place for 8^9+6
8^1 = 8....8^2=64....8^3=(unitplace)2........8^4=(unitplace)6.....8^5=(unitplace)8....so on......again
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closest number to 75 which is divisible by 4 is 76.... therefore 7^76 will have 1 at unit place.........
.that means it will be 3 at the 75th power....so 3+6 will give '9' at unit place for the final answer
for example if we want to find out unit place for 8^9+6
8^1 = 8....8^2=64....8^3=(unitplace)2........8^4=(unitplace)6.....8^5=(unitplace)8....so on......again
...