1. **State the problem:** Calculate $2^{100^{100}}$. 2. **Understand the expression:** The expression $2^{100^{100}}$ means 2 raised to the power of $100^{100}$. 3. **Evaluate the exponent:** $100^{100}$ is a very large number, which means the exponent itself is huge. 4. **Rewrite the expression:** The expression is $2^{100^{100}}$ and cannot be simplified further in a closed form. 5. **Interpretation:** This is an extremely large number, far beyond typical computation or representation. **Final answer:** $2^{100^{100}}$