Dividing Exponential Expressions

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  • 0:03 So, What is an…
  • 0:45 Division of Exponents…
  • 3:03 What if the Terms Have…
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Instructor: Jennifer Beddoe

Jennifer has an MS in Chemistry and a BS in Biological Sciences.

Any time you work with expressions that contain exponents, you have to follow a specific set of rules that are not the same as when you are working with expressions that do not contain exponents. This lesson will describe the rules associated with dividing terms that contain exponents.

So, What Is an Exponent Anyway?

An exponent is a number written as a superscript to another number. It looks like this: 23 or 2^3

The exponent of a number tells you how many times to multiply that number to itself. So, in the earlier example, 2^3 means 2*2*2, which is equal to 8. Using the caret or ^ symbol is another way to write an exponent that can be easier when typing.

Exponents make large multiplication problems easier to write. So, 7*7*7*7*7 = 75, because the equation is asking you to multiply 7 to itself 5 times.

Division of Exponents Means Subtraction

There are certain laws that govern working with exponents. The rule dealing with dividing expressions containing exponents is what this lesson is all about.

When you have two exponential expressions that have the same base, you can easily divide one from another. All you have to do in this instance is subtract the exponent of the denominator (the bottom number of a fraction) from the exponent of the numerator (the top number of a fraction).

Here's an example: 57 / 52. To simplify this expression, just subtract the exponents: 7 - 2 = 5. So, the answer is 55.

Let's look at how this works. If we write out the multiplication of each exponent we get:

(5*5*5*5*5*5*5) / (5*5)

Two of the fives in the numerator will cancel out with the two fives in the denominator, which leaves us with:


To write this with exponents, we just count up the number of fives - there happen to be 5 of them - so the simplified answer is 55.

This simplification works with all exponential expressions where the base is the same for each term. If the base is different, no simplification can be done.

Let's try another example: Simplify y8 / y6. Just like before, to simplify this expression, just subtract the exponents: 8 - 6 = 2, so y8 / y6 = y2.

The rule also applies if one or more of the exponents are negative. Simplify b-2 / b6. Again, just subtract the exponents, making sure to subtract them in the proper order. -2 - 6 = -8. So, b-2*b6 = b-8.

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