Call Now to Set Up Tutoring:

(888) 888-0446

Pre-Algebra : Product Rule of Exponents

Study concepts, example questions & explanations for Pre-Algebra

Create An Account

All Pre-Algebra Resources

11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Product Rule Of Exponents

Simplify:

$3x^{2}2y^{7}\times 5x^{5}y^{3}$

Possible Answers:

$30x^{10}y^{21}$

$30x^{7}y^{10}$

$30xy^{17}$

$30x^{17}y$

$15x^{7}2y^{10}$

Correct answer:

$30x^{7}y^{10}$

Explanation:

When multiplying variables with exponents, we must remember the Product Rule of Exponents: $x^{m}*x^{n}=x^{m+n}$

Step 1: Reorganize the terms so the terms are together:

$3x^{2}2y^{7}\times 5x^{5}y^{3} = 3\times2\times5\times x^{2} \times x^{5}\times y^{7} \times y^{3}$

Step 2: Multiply $3\times2\times5$ :

$30\times x^{2}\times x^{5}\times y^{7}\times y^{3}$

Step 3: Use the Product Rule of Exponents to combine $x^{2}$ and $x^{5}$ , and then $y^{3}$ and $y^{7}$ :

$30\times x^{7}\times y^{10}$

$30x^{7}y^{10}$

Report an Error

Example Question #1 : Product Rule Of Exponents

Simplify the following.

$(x^{2})(x^{5})$

Possible Answers:

$x^{7}$

$x^{-3}$

$x^{10}$

$x^{3}$

Correct answer:

$x^{7}$

Explanation:

The Product of Powers Property states when we multiply two powers with the same base, we add the exponents.

In this case, the exponents are 2 and 5

$x^{2+5}=x^{7}$

Report an Error

Example Question #2 : Product Rule Of Exponents

Simplify the following expression:

6a^2b(2b^3)

Possible Answers:

8a^2b^3

8a^2 + 8b^4

12a^2b^4

12a^2b^3

Correct answer:

12a^2b^4

Explanation:

The exponent represents how many times the term is being multiplied. So, for example, x^2 means (x)(x) and x^5 would be (x)(x)(x)(x)(x)

So the first term 6a^2b = 6 (a)(a)(b)

And the second term 2b^3 =2(b)(b)(b)

Since the two terms are only separated by parentheses, they are being all multiplied together.

First multiply the coefficients, 6(2)=12

We also have a total of 4 's and 2 's all being multipled together.

The final answer is 12a^2b^4

Report an Error

Example Question #2 : Product Rule Of Exponents

Simplify the following expression:

(-2t^7s)(-5ts^3)

Possible Answers:

-10t^7s^3

10t^8s^4

-7t^8 + s^4

-7t^7s^3

Correct answer:

10t^8s^4

Explanation:

The exponent represents how many times the term is being multiplied. So, for example, x^2 means (x)(x) and x^5 would be (x)(x)(x)(x)(x)

So the first term -2t^7s = -2(t)(t)(t)(t)(t)(t)(t)(s)

And the second term -5ts^3 = -5(t)(s)(s)(s)

Since the two terms are only separated by parentheses, they are being all multiplied together.

First multiply the coefficients, (-2)(-5)=10

We also have a total of 8 's and 4 's all being multipled together.

The final answer is 10t^8s^4

Report an Error

Example Question #3 : Product Rule Of Exponents

Simplify the following expression:

(7x^2)(3xy^5)

Possible Answers:

21x^3y^5

10x^3y^5

x^3 + y^5 + 10

21x^2y^5

Correct answer:

21x^3y^5

Explanation:

In the last few problems, we saw one way to multiply terms with exponents.

Another way to explain what we did is to say: "When you MULTIPLY terms together, simplify by ADDING the exponents of each variable."

Here's what that looks like in this case:

First multiply the coefficients: 7(3) = 21

Then ADD the exponents of the variables to simplify. In the first term, the exponent on the is 2. In the second term the exponent is 1. So we ADD 2 + 1 = 3 and have x^3 .

Only the second term has the variable and its exponent is 5. There is nothing to add onto that (because there are no 's in the first term), so it stays y^5 .

Remember, this is all being multiplied together, so the final answer is 21x^3y^5

Report an Error

Example Question #1 : Product Rule Of Exponents

Simplify the following expression:

(5x^2y^3z^2)(-4xy^6z^2)

Possible Answers:

-20x^2y^1^8z^4

x^2y^1^8z^4

-20x^3y^9z^4

-9x^2y^9z^2

Correct answer:

-20x^3y^9z^4

Explanation:

(5x^2y^3z^2)(-4xy^6z^2)

Remember the rule:

"When you MULTIPLY terms together, simplify by ADDING the exponents of each variable."

Here's what that looks like in this case:

First multiply the coefficients: 5(-4)=-20

Then ADD the exponents of the variables to simplify. In the first term, the exponent on the is 2. In the second term the exponent is 1. So we ADD 2+1=3 and just have x^3 .

In the first term, the exponent on the is 3. In the second term the exponent is 6. So we ADD 3+6=9 and just have y^9 .

In the first term, the exponent on the is 2. In the second term the exponent is 2. So we ADD 2+2=4 and just have z^4 .

Remember, all these parts are being multiplied together, so the final answer is -20x^3y^9z^4

Report an Error

Example Question #3 : Product Rule Of Exponents

Simplify the following expression:

4y^4(-4xy^2)

Possible Answers:

-16xy^6

-16 + xy^8

-16x^8y^8

Correct answer:

-16xy^6

Explanation:

The exponent represents how many times the term is being multiplied. So, for example, x^2 means (x)(x) and x^5 would be (x)(x)(x)(x)(x)

So the first term 4y^4 = 4(y)(y)(y)(y)

And the second term -4xy^2= -4(x)(y)(y)

Since the two terms are only separated by parentheses, they are being all multiplied together.

First multiply the coefficients, 4(-4) = -16

We also have a total of 6 's and 1 all being multipled together.

The final answer is -16xy^6

Report an Error

Example Question #7 : Product Rule Of Exponents

Simplify the following expression:

2x^2(-3x^3)

Possible Answers:

-6x - 23

-6x^6

-6x^5

Correct answer:

-6x^5

Explanation:

The exponent represents how many times the term is being multiplied. So, for example, x^2 means (x)(x) and x^5 would be (x)(x)(x)(x)(x)

So the first term 2x^2 = 2(x)(x)

And the second term -3x^3 = -3(x)(x)(x)

Since the two terms are only separated by parentheses, they are being all multiplied together.

First multiply the coefficients, 2(-3) = -6

We also have a total of 's all being multipled together.

The final answer is -6x^5

Report an Error

Example Question #4 : Product Rule Of Exponents

Simplify:

$\left (5t^{3} \right )^{ 3}$

Possible Answers:

$125 t^{3}$

$1 5 t^{9}$

$125 t^{9}$

$125 t^{6}$

$1 5 t^{6}$

Correct answer:

$125 t^{9}$

Explanation:

$\left (5t^{3} \right )^{ 3} = 5^{ 3} \cdot \left (t^{3} \right ) ^{ 3} = 125 t^{3 \cdot 3} = 125 t^{9}$

Report an Error

Example Question #1 : Product Rule Of Exponents

Which of the following is equal to $3x^2\times 4x^3$ ?

Possible Answers:

$\small 6x^6$

` $\small 12x^6$

$\small 12x^5$

$\small 6x^5$

$\small 7x^5$

Correct answer:

$\small 12x^5$

Explanation:

Remember that when multiplying variables with exponents, the following property holds true:

$x^a\times x^b = x^{a+b}$

With this knowledge, we can solve the problem:

$3x^2\times 4x^3$

$=(3\times 4)x^2^+^3$

$\small =12x^5$

The answer is $\small 12x^5$ .

Report an Error

View Pre-Algebra Tutors

Tajrin
Certified Tutor

CUNY Brooklyn College, Bachelor of Science, Computer Science.

View Pre-Algebra Tutors

Abhisek
Certified Tutor

University of Florida, Bachelor of Engineering, Computer Science.

View Pre-Algebra Tutors

Richard
Certified Tutor

CUNY Brooklyn College, Bachelor of Science, Chemistry. CUNY Brooklyn College, Master of Arts, Experimental Psychology.

All Pre-Algebra Resources

11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

GRE Tutors in San Diego, LSAT Tutors in Washington DC, LSAT Tutors in Chicago, ISEE Tutors in Boston, English Tutors in Chicago, ACT Tutors in Miami, ACT Tutors in Dallas Fort Worth, MCAT Tutors in Miami, MCAT Tutors in Seattle, ISEE Tutors in New York City

Popular Courses & Classes

ISEE Courses & Classes in Houston, ISEE Courses & Classes in Washington DC, GMAT Courses & Classes in Houston, ISEE Courses & Classes in Los Angeles, LSAT Courses & Classes in Denver, GRE Courses & Classes in Washington DC, SSAT Courses & Classes in Seattle, Spanish Courses & Classes in Philadelphia, ACT Courses & Classes in Atlanta, GMAT Courses & Classes in Los Angeles

Popular Test Prep

GRE Test Prep in Washington DC, GRE Test Prep in Seattle, GRE Test Prep in Phoenix, LSAT Test Prep in Seattle, MCAT Test Prep in Philadelphia, LSAT Test Prep in San Diego, SAT Test Prep in New York City, GRE Test Prep in Chicago, GMAT Test Prep in Chicago, ACT Test Prep in Washington DC

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Pre-Algebra : Product Rule of Exponents

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #1 : Product Rule Of Exponents

Example Question #1 : Product Rule Of Exponents

Example Question #2 : Product Rule Of Exponents

Example Question #2 : Product Rule Of Exponents

Example Question #3 : Product Rule Of Exponents

Example Question #1 : Product Rule Of Exponents

Example Question #3 : Product Rule Of Exponents

Example Question #7 : Product Rule Of Exponents

Example Question #4 : Product Rule Of Exponents

Example Question #1 : Product Rule Of Exponents

All Pre-Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: