Compare (-1)^100 and -1^100: Exponent Rule Challenge

Which is larger?

$(-1)^{100}⬜-1^{100}$

To determine which is larger between $(-1)^{100}$ and $-1^{100}$, follow these steps:

• Step 1: Evaluate $(-1)^{100}$.
  Since 100 is an even number, $(-1)^{100}$ simplifies to $(-1)$ multiplied by itself 100 times. Even powers of -1 result in $1$, so $(-1)^{100} = 1$.
• Step 2: Evaluate $-1^{100}$.
  Notice that $-1^{100}$ is simply putting a negative sign in front of $1^{100}$. Since powers of 1 are always 1, $1^{100} = 1$, resulting in $-1^{100} = -1$.
• Step 3: Compare the results.
  From our calculations, $(-1)^{100} = 1$ and $-1^{100} = -1$. Comparing these, $1 > -1$.

Thus, the expression $(-1)^{100}$ is greater than $-1^{100}$.

Therefore, the correct comparison is $(-)^{100} > -1^{100}$.

The correct choice from the possible answers is $>$.