Answer
$x^{-n}$ will be negative when:
$n$ is an odd integer and $x$ is a negative integer
Work Step by Step
RECALL:
$x^{-n}=\dfrac{1}{x^n}, x \ne 0$
Note that when $n$ is even, the value of $\dfrac{1}{x^n}$ where $x\ne0$ will always be positive regardless of the value of $x$.
$\dfrac{1}{x^n}$ will only be a negative integer if $n$ is an odd integer and $x$ a is negative integer.
Example:
$(-5)^{-3} = \dfrac{1}{(-5)^3} = \dfrac{1}{-125} = -\dfrac{1}{125}$
Thus, $x^{-n}$ will be negative when $n$ is odd and $x$ is a negative integer.
