# Algebra 1 : How to divide monomial quotients

## Example Questions

### Example Question #85 : Monomials

Divide the following monomial quotients:

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

2. Divide the variables. We also need to remember the following laws of exponents rule: When dividing variables, subtract the exponents.

Combine these to get the final answer:

### Example Question #86 : Monomials

Divide:

Explanation:

In order to simplify this fraction, write the factors out for the numerator and denominator.

Cancel out the common terms in the numerator and denominator.

### Example Question #87 : Monomials

Evaluate:

Explanation:

We can simplify this monomial by cancelling out like terms in the numerator and denominator:

### Example Question #88 : Monomials

Evaluate:

Explanation:

To evaluate, we must cancel out like values on the numerator and denominator:

### Example Question #89 : Monomials

Divide the following

Explanation:

To solve, we will divide the monomials using the quotient of powers.

## SOLUTION A

We have

We know

and

and so on.

Let's expand the original problem.  We get

Now, we know we can look at the numerator and cancel anything in the denominator.  So,

We can cancel the variables that have been highlighted.  So, we get

We can divide the integers, leaving us with

Which equals

## SOLUTION B

We can solve this a different way by using a shortcut.  When dividing monomials, simply subtract the quotients with the same base.

The different variables have been highlighted.  Now, we subtract.

### Example Question #90 : Monomials

Find the quotient of the following

.

Explanation:

When dividing polynomials, you subtract the powers with the same base.

We know that anything raised to the zero power equals 1.

So we get

We simplify the integers.

We get

### Example Question #41 : How To Divide Monomial Quotients

Divide the monomials:

Explanation:

In order to simplify this expression, write out the factors of the numerator and denominator.

Cancel out the common terms on the numerator and denominator.

### Example Question #42 : How To Divide Monomial Quotients

Simplify the following:

Explanation:

When dividing monomials, we divide the coefficients, and if the base is the same, we subtract the exponents.  So

can be simplified to

### Example Question #43 : How To Divide Monomial Quotients

Divide the monomials:

Explanation:

The terms in the numerator and denominator can be expanded.

Write out the terms and factors in order to see what can be cancelled on the numerator and denominator.

After cancelling out the common terms, we are left with .

### Example Question #44 : How To Divide Monomial Quotients

Divide the following monomials: