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# Finding Negative Exponents in Algebra

(KS3, Year 7)

## 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

**.**

^{1}⁄_{an}This is a laws of exponents.

## How to Find Negative Exponents in Algebra

## Question

Use the law of exponents to find the power with the negative exponent below.## Step-by-Step:

# 2

# 3

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

## Answer:

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**and^{-−n}**a**are^{n}**powers**. -
The
**bases**of the powers are**a**. -
The
**exponent**of**a**is^{−n}**−n**and the exponent of**a**is^{n}**n**. -
The fraction
is the reciprocal of^{1}⁄_{an}**a**.^{n}

## 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, a^{2}means that a is multiplied by itself

**2**times:

a

^{2}= 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.

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