[ Decimal numeral system ] [ Divisibility rules for 3 and 9 ]

For the number $2^{100}$, the sum of its digits was found, then the sum of the digits of the result, and so on. Eventually, a single-digit number was obtained. Find it.
$2^{100}=\left(2^{6}\right)^{16} \cdot 2^{4} \equiv 1^{16} \cdot 16 \equiv 7(\bmod 9)$.

## Answer

7.