Solve the Equation: Finding the Value Equal to -100

To solve this problem, follow these steps:

• Step 1: Identify that the problem involves finding a mathematical expression that equals $-100$.
• Step 2: Consider how negative powers and negative bases interact with parentheses.
• Step 3: Evaluate each choice using the properties of powers.

Now, let's evaluate each choice:

Choice 1: $(-1)^{100}$
Computing: $(-1)^{100}$ equals $1$, since $100$ is even and any even power of $-1$ results in $1$. Therefore, this choice cannot be $-100$.

Choice 2: $(-10)^2$
Computing: $(-10)^2$ equals $100$, as squaring a negative number results in a positive number. Thus, this choice cannot be $-100$.

Choice 3: $-(-10)^2$
Computing: $-(-10)^2$ means first computing $(-10)^2$, which is $100$, and then applying the negative sign resulting in $-100$. Therefore, this correctly matches $-100$.

Choice 4: $1^{100}$
Computing: $1^{100}$ is $1$, as any number raised to any power remains itself when the base is $1$. Thus, it cannot equal $-100$.

Therefore, the correct choice is $-(-10)^2$, as it evaluates directly to $-100$.