## The Lesson

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.

## Question

Use the law of exponents to find the power with the negative exponent below. # 1

Write 1 on top of a fraction (called the numerator). # 2

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

## Lesson Slides

The slider below shows another real example of how to find negative exponents. Open the slider in a new tab

## 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. 