## 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

**. This is a laws of exponents.**

^{1}⁄_{an}## 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

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.

## 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