# Dividing Monomials

How Do We Divide When Exponents are Involved?

As you've seen in the prior lessons, when we work with monomials, we
see a lot of exponents.

You've discovered the laws of exponents and the
properties for multiplying exponents, but what happens when we divide?
That is the question we are going to answer in this lesson.

Let's start by taking a look at a few problems in "expanded form".
Once you examine these examples, you'll discover the rule on your own.

## Expanded Form Examples

Take a look at the exponents in the original problem and then analyze
the exponents in the answer for each example.

Can you figure out the
rule for exponents when you are dividing?

## Dividing Monomials

When you ** divide** powers that have the **same base**, you **subtract** the exponents.

That's a pretty easy rule to remember! It's the opposite of the
multiplication rule.

When you multiply powers that have the same base,
you add the exponents and when you divide powers that have the same
base, you subtract the exponents.

Let's look at a couple of examples.

## Example 1: Dividing Monomials

And.... another example.

## Example 2

That's a pretty easy rule to remember! Let's take a look at one more
property. This property is called, Power of a Quotient Property.

So, what is a quotient?

## Quotient

A Quotient is an answer to a division problem.

Let's take a look at what happens when you raise a fraction (or a
division problem) to a power.

Remember: A division bar and fraction
bar are synonymous!

## Power of a Quotient Property

To find the power of a quotient, raise the numerator to the power, and the denominator to the power. Then divide.

Let's take a look at a few examples.

## Power of a Quotient: Example 1

Power of a Quotient: Example 2

You may now be ready to move onto the next lesson which is simplifying monomials.

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