1. The problem is to understand why $4$ is not written as $2^2$ in a certain context. 2. The number $4$ can indeed be expressed as $2^2$ because $2$ multiplied by itself equals $4$. 3. The expression $4 = 2^2$ is a valid equality and is often used to show that $4$ is a perfect square. 4. Sometimes, depending on the problem or context, it might be simpler or more appropriate to use the number $4$ directly instead of its exponential form $2^2$. 5. Using $2^2$ emphasizes the factorization or the base number and exponent, which is useful in problems involving powers, roots, or logarithms. 6. In summary, $4$ and $2^2$ represent the same value, and the choice between them depends on the context and what is more convenient for the problem at hand.