Graduate Management Admission Test (GMAT) Practice Test

What is the result when a negative number is raised to an odd exponent?

1. Zero

2. Positive

3. Negative

4. Undefined

The correct answer is: Negative

When a negative number is raised to an odd exponent, the result is negative. This occurs because multiplying a negative number an odd number of times continues to produce a negative result. For example, if you take -2 and raise it to the third power (-2 × -2 × -2), the first two multiplications yield a positive outcome of 4, but then multiplying by -2 again gives a negative result of -8. This pattern holds for any negative number raised to any odd exponent; the last multiplication by the negative base ensures that the overall result remains negative. Hence, since the question specifies raising a negative number to an odd exponent, the correct conclusion is that the result will indeed be negative.