1. The problem is to calculate $2^{100}$. 2. The formula used is the exponentiation rule: $a^n$ means multiplying $a$ by itself $n$ times. 3. Here, $a=2$ and $n=100$, so we multiply 2 by itself 100 times. 4. Direct calculation of $2^{100}$ results in a very large number. 5. Using a calculator or software, $2^{100} = 1267650600228229401496703205376$. 6. Therefore, the value of $2^{100}$ is $1267650600228229401496703205376$.