Categories

# How to divide exponents

How to divide exponents.

• Dividing exponents with same base
• Dividing exponents with different bases
• Dividing negative exponents
• Dividing fractions with exponents
• Dividing fractional exponents
• Dividing variables with exponents

### Dividing exponents with same base

For exponents with the same base, we should subtract the exponents:

3 4 / 3 2 = 3 4-2 = 3 2 = 3⋅3 = 9

### Dividing exponents with different bases

When the bases are different and the exponents of a and b are the same, we can divide a and b first:

a n / b n = (a / b) n

8 4 / 4 4 = (8/4) 4 = 2 4 = 2⋅2⋅2⋅2 = 16

When the bases and the exponents are different we have to calculate each exponent and then divide:

10 2 / 5 3 = 100 / 125 = 0.8

### Dividing negative exponents

For exponents with the same base, we can subtract the exponents:

a -n / a -m = a -n-(-m) = a m-n

3 -4 / 3 -6 = 3 6-4 = 3 2 = 3⋅3 = 9

When the bases are different and the exponents of a and b are the same, we can multiply a and b first:

a -n / b -n = (a/b) -n = 1 / (a/b) n = (b/a) n

2 -2 / 3 -2 = (2/3) 2 = 0.44

When the bases and the exponents are different we have to calculate each exponent and then divide:

a -n / b -m = b m / a n

2 -3 / 5 -2 = 5 2 / 2 3 = 25 / 8 = 3.125

### Dividing fractions with exponents

Dividing fractions with exponents with same fraction base:

(a / b) n / (a / b) m = (a / b) n-m

(6/2) 4 / (6/2) 3 = (6/2) 4-3 = (6/2) 1 = 3

Dividing fractions with exponents with same exponent:

(a / b) n / (c / d) n = ((a / b)/(c / d)) n = ((a⋅d / b⋅c)) n

(6/2) 2 / (4/2) 2 = ((6/2)/(4/2)) 2 = ((6⋅2)/(2⋅4)) 3 = (12/8) 3 = 3.375

Dividing fractions with exponents with different bases and exponents:

(10/5) 4 / (9/3) 3 = 16 / 27 = 0.592

### Dividing fractional exponents

Dividing fractional exponents with same fractional exponent:

a n/m / b n/m = (a / b) n/m

6 4/2 / 3 4/2 = (6/3) 4/2 = 2 4/2 = √(2 4 ) = √16 = 4

Dividing fractional exponents with same base:

a n/m / a k/j = a (n/m) -(k/j)

4 3/2 / 4 4/3 = 4 (3/2) -(4/3) = 4 (1/6) = 6 √4 = 1.259

Dividing fractional exponents with different exponents and fractions:

3 3/2 / 3 4/3 = √(3 3 ) / 3 √(3 4 ) = 5.19 / 4.32 = 1.2

### Dividing variables with exponents

For exponents with the same base, we can subtract the exponents:

x 3 / x 2 = (x⋅x⋅x) / (x⋅x) = x 3-2 = x 1

Image Source: http://www.mycompasstest.com

In this lesson we look at how to Divide Algebra Expressions which contain exponents.

We also introduce the Dividing Exponents “Subtraction” short cut rule.

If you are very new to Exponents, we recommend that you first do our previous Exponents Lessons, which are accessable at the following links:

In our previous lesson on Algebra Dividing, we looked at dividing exponent terms by fully expanding out and cancelling identical terms, as in this example: Image Copyright 2013 by Passy’s World of Mathematics

Exponents “Subtract Powers” Dividing Rule

Rather than do lengthy expansions and cancelling out, we can use a shortcut rule for doing our Exponent Division.

This shortcut rule is similar to the “Add Powers Rule” which we have learned previously for Multiplying Exponents. Image Copyright 2013 by Passy’s World of Mathematics

The following example shows how to do our previous question using the Dividing – Subtract Powers Rule. Image Copyright 2013 by Passy’s World of Mathematics

The Subtract Rule also works for Expressions containing letter variables. Image Copyright 2013 by Passy’s World of Mathematics

The following quick video shows how to do dividing that involves exponents, using the subtraction rule.

The following video shows three examples of dividing exponents.

Steps for Dividing Exponents

For the more involved expressions we will be doing in the remainder of this lesson, the following working out steps need to be followed: Image Copyright 2013 by Passy’s World of Mathematics

Dividing Exponents Examples

The following example shows how to break apart and simplify a multiple items exponents division fraction. Image Copyright 2013 by Passy’s World of Mathematics

This next example shows how to do an exponents division which involves negative numbers. Image Copyright 2013 by Passy’s World of Mathematics

If you enjoyed this lesson, why not get a free subscription to our website.

To find out exactly how free subscription works, click the following link:

If you would like to submit an idea for an article, or be a guest writer on our website, then please email us at the hotmail address shown in the right hand side bar of this page.

If you are a subscriber to Passy’s World of Mathematics, and would like to receive a free PowerPoint version of this lesson, that is 100% free to you as a Subscriber, then email us at the following address:

Please state in your email that you wish to obtain the free subscriber copy of the “Dividing Exponents” Powerpoint.

Help Passy’s World Grow

Each day Passy’s World provides hundreds of people with mathematics lessons free of charge.

Help us to maintain this free service and keep it growing.

Donate any amount from \$2 upwards through PayPal by clicking the PayPal image below. Thank you!

PayPal does accept Credit Cards, but you will have to supply an email address and password so that PayPal can create a PayPal account for you to process the transaction through. There will be no processing fee charged to you by this action, as PayPal deducts a fee from your donation before it reaches Passy’s World.

Exponent Rules Dividing Exponents with like bases
There are two rules to remember when you are dividing exponents with like bases.
Divide the coefficients
Subtract the exponents

Today we are going to look at the Rules for Exponents when you are dividing.
Ok here we have 2 ^4divided by2^2.
Since we have like bases we can just subtract the exponents.

We are really just looking for like bases. 2^4 minus 2 which equals 2 squared and that simplifies to 4 if you need an integer.

Here is another example of dividing two exponents.
We have 2^6/2^4 which equals 6 -4 which equals 2 squared, which equals 4.
Now let’s look at some additional problems 8x^5 divided by x^4

Since we don’t have a coefficient to divide we will just imagine there is a 1 in front of the x^4 so x^5-x^4 equals x to the first power.

Let’s now try one with a coefficient. We have 15x^7 divided by 5x^2.
Step 1 is to divide the coefficients, and then get x^7 -x^2 which means you subtract 2 so you end up with 3x^5
The rule is you divide the coefficients and subtract the exponents.
Let’s look at one more problem in which you divide exponents
8b^7 divided by b^4
The 8 stays an 8 because you are dividing by one and b^7-4 =3 so the answer will be 8b^3
So this is how you simplify exponents when are dividing.

How to divide exponents. When dividing exponents you divide the coefficient and subtract the exponent.

Cuemath’s Dividing Exponents Calculator is an online tool that helps to find the division of two numbers with exponent values.

## What is Dividing Exponents Calculator?

Cuemath’s online Dividing Exponents calculator helps you to divide the two numbers with exponent values within a few seconds.

## How to Use Dividing Exponents Calculator?

• Step 1: Enter the base number, exponent number 1, and exponent number 2 in the given input box.
• Step 2: Click on the “Divide” button to divide the two numbers with exponent values.
• Step 3: Click on the “Reset” button to divide for different numbers and different exponent values.

## How to Find Dividing Exponents?

An exponent is defined as the number of times to multiply the base number by itself. In simple terms, how many times a particular number is multiplying to itself, is shown by using exponents.

Note: 1) To multiply powers with the same base, keep the base and add the exponents. For example: 4 3 × 4 2 = 4 3+2 = 4 5

2) When you are dividing two powers with the same base, subtract the exponent of the denominator from the exponent of the numerator to give you the exponent of the answer. For example: 5 6 ÷ 5 3 = 5 6-3 = 5 3. ### Solved Example:

Divide 7 4 and 7 1 .

### Solution:

= 7 4 / 7 1 [As the base value are equal, divide powers with the same base, keep the base and subtract the exponents]

Similarly, you can try for dividing exponents