Negative Exponents Explained

A negative exponent tells you to move the base across the fraction bar. Once the base moves, the exponent becomes positive. Although negative exponents can look confusing at first, they follow a simple movement rule that makes rewriting expressions much easier.

How It Works

Step 1

Find the negative exponent

Look for the exponent with a minus sign. This tells you which number needs to move.

$$2^{-3}$$

Step 2

Move the base to the other side of the fraction

The number with the negative exponent moves across the fraction bar.

$$2^{-3}=\frac{1}{2^3}$$

Step 3

Make the exponent positive

Once the base moves, the exponent becomes positive automatically.

This works the same way even if the negative exponent starts in the denominator.

$$\frac{1}{7^{-2}}=7^2$$

Try These Examples

Rewrite the expression using positive exponents: $$4^{-1}$$

$$
\frac{1}{4}
$$

The base moves to the denominator and the exponent becomes positive.

Rewrite the expression: $$\frac{1}{7^{-2}}$$

$$7^2$$

Because the negative exponent is in the denominator, the base moves to the numerator.

Watch Out

Common Mistake

A negative exponent does not make the value negative.

The negative sign tells you to move the base across the fraction bar, not to change its sign.

$$
2^{-3} = \frac{1}{8}
$$

$$
2^{-3} \neq -8
$$

A negative exponent does not make the value negative.

The negative sign tells you to move the base across the fraction bar, not to change its sign.

$$
2^{-3} = \frac{1}{8}
$$

$$
2^{-3} \neq -8
$$

Keep Practicing

Try these related worksheets to build fluency and confidence.