# Negative Exponent

How to solve the negative exponent a^{-m}: formula, 3 examples, and their solutions.

## Formula

### Formula

a^{-m} = 1/a^{m}

(a ≠ 0)

The minus sign in the exponent means the reciprocal.

So switch the position of the power:

from the numerator to the denominator,

or from the denominator to the numerator.

## Example 1

### Example

### Solution

x^{-4} = x^{-4}/1

x^{-4} is in the numerator.

So move the power to the denominator.

So x^{-4} = 1/x^{4}.

## Example 2

### Example

### Solution

x^{-3} is in the denominator.

So move the power to the numerator.

So 1/x^{-3} = x^{3}/1.

So x^{3} is the answer.

## Example 3

### Example

Change the negative exponents by moving the powers.

### Solution

x^{-5} is in the numerator.

So move the power to the denominator.

So write x^{5} in the denominator.

Write y^{7} in the numerator.

Write x^{2} in the denominator.

y^{-1} is in the denominator.

So move the power to the numerator.

So write y (= y^{1}) in the numerator.

So the given expression is (y^{7}⋅y)/(x^{5}⋅x^{2}).

y^{7}⋅y = y^{8}

x^{5}⋅x^{2} = x^{7}

Product of Powers

So y^{8}/x^{7} is the answer.