The conversation between human and AI assistant.
What are the last two digits in [math]2^{2016}[/math]?
How did you calculate it?
I used the pattern method for finding the last two digits in the powers of 2. The pattern goes like this: the last two digits in 2^1 are 02, in 2^2 are 04, in 2^3 are 08, and so on. If we continue this pattern, we see that the last two digits in 2^6 are 64, in 2^7 are 28, in 2^8 are 56, in 2^9 are 12, and so on. Since 2016 is divisible by 4, we can see that 2^2016 has the same last two digits as 2^4, which is 16. Therefore, the last two digits in 2^2016 are 76.