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# Finding an Exponent of −1 in Algebra

(KS3, Year 8)

## 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

**.**

^{1}⁄_{a}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.## Step-by-Step:

# 1

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

**x**.# 3

## Answer:

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:-
**a**is a^{ −1}**power**. -
The
**base**of the power is**a**. -
The
**exponent**is**−1**. -
The fraction
is the reciprocal of^{1}⁄_{a}**a**.

## 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.

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