The conversation between human and AI assistant.
What are the last two digits in [math]2^{2016}[/math]?
How did you calculate that?
I used the same pattern method for finding the last two digits. The pattern goes like this: the last two digits in 3^1 are 03, in 3^2 are 09, in 3^3 are 27, in 3^4 are 81, and so on. If we continue this pattern, we see that the last two digits in 3^6 are 49, in 3^7 are 47, in 3^8 are 41, in 3^9 are 23, and so on. Since 2016 is divisible by 4, we can see that 3^2016 has the same last two digits as 3^4, which is 81. Therefore, the last two digits in 3^2016 are 01.