# Finding Negative Exponents in Algebra

A power with a negative exponent is equal to the reciprocal of the power (1 over the power) with the exponent made positive.

Imagine we have the letter a with an exponent of -n. We put the whole power under 1 and remove the minus sign from the exponent. This is equal to 1an.

This is a laws of exponents.

# How to Find Negative Exponents in Algebra

#### An Example Question

Use the law of exponents to find the power with the negative exponent below.

Step 1

Write 1 on top of a fraction (called the numerator).

Step 2

Write the power from the question on the bottom of the fraction (called the denominator).

Step 3

Remove the minus sign from the exponent. In our example, the exponent of -2 becomes 2.

We have found the negative exponent.

# Understanding Finding a Negative Exponent in Algebra

Let us look at the rule for negative exponents in algebra:

• a-n and an are powers.

• The bases of the powers are a.

• The exponent of a-n is -n and the exponent of an is n.

• The fraction 1an is the reciprocal of an.

# Real Example of How to Find Negative Exponents in Algebra

The slider below shows another real example of how to find negative exponents.

Algebra Lessons
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# What Is an Exponent?

An exponent tells you how many times a number or letter is multiplied by itself.

An exponent is denoted by a raised number by the right hand side of the number (called the base) that is multiplied by itself.

For example, a2 means that a is multiplied by itself 2 times:

a2 = a × a

# What Is a Reciprocal?

A reciprocal of a quantity (such as a letter or power) is 1 divided by the quantity.

# Reciprocals With Coefficients

What if there is a number or other letter written in front of a power with a negative exponent?

The number or letter in front is a coefficient that is multiplying what comes after it. It goes on top of the fraction instead of 1.