# Algebra 1 : How to divide monomial quotients

## Example Questions

### Example Question #11 : Simplifying Exponents

Simplify the rational expression.

Explanation:

To simplify variables with exponents through division, you must subtract the exponent in the denominator from the numerator.

Remember that negative exponents will eventually be moved back to the denominator.

### Example Question #78 : Expressions

Divide the fractions.

Explanation:

Dividing fractions is equal to multiplying by the reciprocal.

Cross-cancel the 30 with the 25, and the 22 with the 11.

Combine via multiplication and simplify.

### Example Question #14 : Simplifying Exponents

Simplify

Explanation:

Rewrite so that you are multiplying the reciprocal of the second fraction:

You can then simplify using rules of exponents:

### Example Question #51 : Monomials

Evaluate:

Explanation:

First, divide the coefficients.

.

Now consider the variables. means x times itself 3 times. Doing is the same as .

We see that an x from the top can cancel with the x on the bottom, leaving , or . Our answer then is .

### Example Question #52 : Monomials

Divide:

Explanation:

Dividing exponents by the same base allows the powers to be subtracted.  Rewrite the exponents as one base.

### Example Question #53 : Monomials

Find the result of

.

Explanation:

The question asks for the quotient of .

We can rewrite the expression using the rules of multiplication and exponents to find the answer of .

### Example Question #61 : Monomials

Divide:

Explanation:

Notice that both bases are the same.  The power of the base in the numerator is one.

Since the bases are divided, simply subtract the powers.

### Example Question #62 : 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 #63 : 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 #64 : Monomials

Divide the following monomial quotients: