# #\$ Negative Numbers with Exponents

## Positive Exponent with a Negative Base

$$(-4)^{3}$$

Because we have a positive 3 in the exponent, we will multiply -4 by itself 3 times.

$$(-4)^{3}= (-4)(-4)(-4)$$

Three negatives multiplied together is a negative.

$$-64$$

## Negative Exponent with a Negative Base

$$(-5)^{-2}$$

$$\frac{1}{5^{2}})$$

$$\frac{1}{5\times5})$$

$$\frac{1}{25})$$

## Fraction Exponent with a Negative Base

$$(-125)^{\frac{1}{3}}$$

$$\sqrt[3]{-125}$$

$$5$$