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

$a$ has to be a negative number, and $n$ has to be an odd number.
If $a$ is positive, $a^{n}$ will always be positive. For $a^{n}$ to be negative, $a$ has to be a negative number. Furthermore, a negative number raised to an even power is always positive. For $a^{n}$ to be negative, $n$ has to be an odd number. Both conditions must be satisfied.