# Algebra 1 : Monomials

## Example Questions

### Example Question #3 : Simplifying Expressions

Simplify:

Explanation:

and  cancel out, leaving  in the numerator. 5 and 25 cancel out, leaving 5 in the denominator

### Example Question #1 : Simplifying Expressions

Simplify the following:

Explanation:

First, let us factor the numerator:

### Example Question #1 : How To Divide Monomial Quotients

Simplify the following:

Explanation:

First, flip the numerator and the denominator of the second fraction to turn the division into multiplication.

We can then cancel like terms.

From both the numerator and denominator, remove one , remove one , and remove one :

Then we finish by multiplying the constants:

### Example Question #11 : Simplifying Exponents

Simplify this expression:

Explanation:

When different powers of the same variable are multiplied, the exponents are added.  When different powers of the same variable are divided, the exponents are subtracted.  So, as an example:

For the above problem,

Therefore, the expression simplifies to:

### 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

.