The conversation between human and AI assistant.
What are the last two digits in [math]2^{2016}[/math]?
Wow, that was quick. Can you explain how you found it?
Of course! The last two digits of [math]2^{2016}[/math] depend only on the last two digits of each power of 2. The last two digits of consecutive powers of 2 form a pattern that repeats every four powers, namely 02, 04, 08, 16, 32, 64, 28, 56, 12, 24, 48, 96. Since 2016 is a multiple of 4, the last two digits are the same as the last two digits of [math]2^{16}[/math], which is 65536. The last two digits of 65536 are 76.