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*

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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:

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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.

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The following example shows how to do our previous question using the Dividing – Subtract Powers Rule.

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The Subtract Rule also works for Expressions containing letter variables.

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Videos about Dividing Exponents

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:

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Dividing Exponents Examples

The following example shows how to break apart and simplify a multiple items exponents division fraction.

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This next example shows how to do an exponents division which involves negative numbers.

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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.

## Dividing Exponents-8th Grade Math

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?

Please follow the below steps to use the dividing exponents calculators:

**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