What is the last digit of 3 raise to 278,885

Question

What is the last digit of 3^278,885?

a. 3

b. 9

c. 7

d. 1

I have answered a) 3. Am I correct?

Answer 1

3^0 = 1

3^1 = 3

3^2 = 9

3^3 = 27

3^4 = 81

3^5 = 81x3 = 243

3^6 = 243x3 =729

3^7 = 729x3 = 2227

3^8 = 2227x3 = 6681

278885/4 = 69721 with remainder 1

3^278885 has the same last digit as 3^8, 3^4 and 3^1 = 3

if the exponent is exactly divisible by 4, the last digit is 1

if the exponent is divisible by 4 with remainder 1, then the last digit is 3

if the exponent is divisible by 4 with remainder 2, the last digit is 9

if the exponent is divisible by 4 with remainder 3, the last digit is 7

the pattern repeats for the last digit every 4 times the exponent increases by 1

1, 3, 9, 7, 1, 3, 9, 7, 1,3, 9, 7, ....

a) 3 You're correct