## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$x^{-n}$ will be negative when: $n$ is an odd integer and $x$ is a negative integer
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.