2 to the 100th power is 1,267,650,600,228,229,401,496,703,205,376. That's 31 digits, a number of about 1.27 × 10^30.
A quick way to check it: 2^10 = 1,024, so 2^100 = (2^10)^10. Doubling repeatedly from 1 gets you there too, and it's a nice exercise because each step is easy to verify by hand. This is exact integer arithmetic, not an estimate, so there's no rounding involved.
If you want to double-check it yourself, any big-integer calculator or a short Python line (print(2**100)) will print the same digits.
If anyone wants to verify the digits independently or see how the number of digits grows with each power of two, add it below.
