Algebra 1 : Monomials

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #3 : Simplifying Expressions

Simplify:        

Possible Answers:

Correct answer:

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:

Possible Answers:

Correct answer:

Explanation:

First, let us factor the numerator:

Example Question #1 : How To Divide Monomial Quotients

Simplify the following:

Possible Answers:

Correct answer:

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:

         

Possible Answers:

Correct answer:

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.

Possible Answers:

Correct answer:

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.

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Correct answer:

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  

Possible Answers:

Correct answer:

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:

Possible Answers:

Correct answer:

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:  

Possible Answers:

Correct answer:

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

.

Possible Answers:

Correct answer:

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 .

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