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# Finding Negative Exponents

(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 number**2**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}⁄_{2n}This is a laws of exponents.

## How to Find Negative Exponents

## 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.

As the final step, evaluate the power with the positive exponent.

# 4

Evaluate the power on the bottom of the fraction. In our example, evaluate

**3**.^{2}
3

^{2}= 3 × 3 = 9## Answer:

We have found the negative exponent.## Understanding Finding a Negative Exponent

Let us look at the rule for negative exponents:-
**2**and^{−n}**2**are^{n}**powers**. -
The
**bases**of the powers are**2**. -
The
**exponent**of**2**is^{−n}**−n**and the exponent of**2**is^{n}**n**. -
The fraction
is the reciprocal of^{1}⁄_{2n}**2**.^{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, 2^{2}means that 2 is multiplied by itself

**2**times:

2

^{2}= 2 × 2## What Is a Reciprocal?

A reciprocal of a quantity (such as a letter or power) is 1 divided by the quantity.**Help Us To Improve Mathematics Monster**

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