Problem
Determine whether each of the following is positive or negative. $-$ $x^{n}$ when $n$ is even and $x$ is positive $x^{n}$ when $n$ is odd and $x$ is negative $x^{n}$ when $n$ is even and $x$ is negative $x^{n}$ when $n$ is odd and $x$ is positive
Solution
Step 1 ：Determine whether each of the following is positive or negative.
Step 2 ：$x^{n}$ when $n$ is even and $x$ is positive: This is \(\boxed{\text{Positive}}\) because a positive number raised to any power is always positive.
Step 3 ：$x^{n}$ when $n$ is odd and $x$ is negative: This is \(\boxed{\text{Negative}}\) because a negative number raised to an odd power is always negative.
Step 4 ：$x^{n}$ when $n$ is even and $x$ is negative: This is \(\boxed{\text{Positive}}\) because a negative number raised to an even power is always positive.
Step 5 ：$x^{n}$ when $n$ is odd and $x$ is positive: This is \(\boxed{\text{Positive}}\) because a positive number raised to any power is always positive.
