## The Lesson

A letter with an exponent of −1 is equal to the reciprocal of the letter (1 divided by the letter). Imagine we have the letter a with an exponent of −1. This is equal to 1a. This is a law of exponents.

## How to Find an Exponent of −1 in Algebra

Finding an exponent of −1 in algebra is easy.

## Question

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

Find the letter or symbol that has an exponent of −1. In our example, the letter is x. # 2

Write 1 on the top of a fraction (called the numerator). # 3

Write the letter from Step 1 (x) on the bottom of the fraction (called the denominator). We have found an exponent of −1. ## Understanding Finding an Exponent of −1 in Algebra

Let us look at the rule for an exponent of −1 in algebra: ## Lesson Slides

The slider below shows another real example of how to find an exponent of −1 in algebra. Open the slider in a new tab

## What Is a Reciprocal?

A reciprocal of a letter is 1 divided by the letter. ## Reciprocal of a Fraction

The reciprocal of a fraction just flips the fraction upside down. ## Reciprocals with Coefficients

What if there is a number or other letter written in front of a letter with an exponent of −1? 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. 