# Chapter 4 - Polynomials - 4.1 Exponents and Their Properties - 4.1 Exercise Set - Page 236: 97

$a$ has to be a negative number, and $n$ has to be an odd number.

#### Work Step by Step

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.

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