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Finding Negative Exponents in Algebra

(KS3, Year 7)

Let's start with a test!

The Test

Here is a -question, multi-choice test for the "Finding Negative Exponents in Algebra" lesson. The pass mark is 90%. Don't worry! All the information you need to pass is in the lesson section under the test.

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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. a to the minus n equals 1 over 2 to the n

a to the minus n equals 1 over 2 to the n

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:

1

Write 1 on top of a fraction (called the numerator). 1 over the line

2

Write the power from the question on the bottom of the fraction (called the denominator). 1 over x to the minus 2

3

Remove the minus sign from the exponent. In our example, the exponent of −2 becomes 2. 1 over x to the 2

Answer:

We have found the negative exponent. 1 over x squared

Understanding Finding a Negative Exponent in Algebra

Let us look at the rule for negative exponents in algebra: bases and exponents

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

Lesson Slides

The slider below shows another real example of how to find negative exponents.

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, a² means that a is multiplied by itself 2 times:

a² = a × a

What Is a Reciprocal?

A reciprocal of a quantity (such as a letter or power) is 1 divided by the quantity. reciprocals of letters

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. 2 over x squared

This page was written by Stephen Clarke.