Question

what is the last digit of 6to the power 100

Answer 1

6

6^ any number, the last digit will always be 6

6^2 = 36

6^3 = 216

6^5 = 7776

Answer 2

The cyclicity of 6 is 1.

Cyclicity of a number is the number of times after which the number repeats itself in a pattern.

6^1=6 (here ‘^’ means to the power)

6^2=36

6^3=216

Look at the unit digit the unit digit is always 6. This is what cyclicity implies so whatever would be the power of 6 it’s unit digit would always be 6. Same is te case with 5 the cyclicity of 5 is also 1. The cyclicity of 4 & 9 is 2. You could verify it by yourself.

So now coming into your question since the cyclicity of 6 is 1 hence the unit digit/last digit of 6^100 =6.