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 #11 : Product Rule Of Exponents

Simplify:

$x^{3}y^{2}\cdot xy^{4}$

Possible Answers:

$x^{4}y^{6}$

$x^{4}y^{8}$

$x^{3}y^{6}$

$x^{3}y^{8}$

Correct answer:

$x^{4}y^{6}$

Explanation:

Use the product rule of exponents, which states that when multiplying expression(s) with the same base, you add the exponents together:

$x^{3+1}y^{4+2}$

Therefore the correct answer is $x^{4}y^{6}$ .

Report an Error

Example Question #12 : Product Rule Of Exponents

Evaluate:

5x(y+3+2x)

Possible Answers:

7x+y+3

5xy +15x+10x^2

5xy +7+7x

25x +15xy

15xy+10x^2

Correct answer:

5xy +15x+10x^2

Explanation:

Distribute the to each of the terms and add them.

5xy +15x +10x^2

Report an Error

Example Question #13 : Product Rule Of Exponents

Simplify: $x^3*x^{-2}$

Possible Answers:

x^5

$x^{-6}$

$x^{-5}$

Correct answer:

Explanation:

The general rule for multiplying terms with exponents is that we add the exponents together. In this case the exponents are and , and -2+3=1 . x^1 is just : anything to the first power is itself.

Report an Error

Example Question #13 : Product Rule Of Exponents

Simplify: x^3*(3x)^2

Possible Answers:

6x^6

9x^5

3x^6

3x^5

6x^5

Correct answer:

9x^5

Explanation:

To simplify x^3*(3x)^2 it helps to understand what it means. x^3 just means x times itself 3 times, x*x*x . (3x)^2 means multiply times itself, or (3x)*(3x) . We can simplify that by multiplying 3*3 = 9 and x*x=x^2 . Multiplying both terms together gives us x*x*x*9*x*x . This is a 9 and 5 x's being multiplied together, or 9x^5 .

Report an Error

Example Question #111 : Polynomials

Simplify: x^3*y^4

Possible Answers:

12xy

This expression is already simplified

(xy)^7

$(xy)^{12}$

x*y^7

Correct answer:

This expression is already simplified

Explanation:

The product rule tells us that if we're multiplying 2 terms with exponents, we add the exponents. However, that is only applicable for 2 terms with the same base. In this case, our bases are different variables, so we can't use the product rule. This expression is as simplified as possible.

Report an Error

Example Question #16 : Product Rule Of Exponents

Use the product rule of exponents to simplify: 5x^6(2x^4)+2y^3(x^2+3x^2)

Possible Answers:

2x^2(5x^8+4y^3)

$10x^{10}+2y^3(3x^2)$

$7x^{2}+2y^3(4x^2)$

None of the other answers.

8x^2(2x^8+y^3)

Correct answer:

2x^2(5x^8+4y^3)

Explanation:

The product rule states that when two like bases with the same power are being multiplied, we add the powers together and preserve the base. In mathematical language, $a^m*a^n=a^{m+n}$ . If constants are present in front of either base we multiply them as usual.

5x^6(2x^4)+2y^3(x^2+3x^2)

Combine using the power rule:

$10x^{10}+2y^3(x^2+3x^2)$

Combine the parenthesis:

$10x^{10}+2y^3(4x^2)$

$10x^{10}+8y^3x^2$

Factor fully:

2x^2(5x^8+4y^3)

Report an Error

Example Question #112 : Polynomials

Simplify the following expression:

$z^{4} \times z^{3} \times z^{-2} \times y^{3}$

Possible Answers:

$z^{-5}y^{3}$

$z^{-24}y^{3}$

$z^{5}y^{-3}$

$z^{5}y^{3}$

$z^{7}y$

Correct answer:

$z^{5}y^{3}$

Explanation:

The product rule of exponents states that we can multiply two exponents with the same base by adding the exponents. The exponents of different bases cannot be summed, therefore our term will not change.

$z^{4} \times z^{3} \times z^{-2} \times y^{3}$

$4 + 3 + \left ( -2\right ) = 5$

Therefore, the simplest form of the expression is

$z^{5} \times y^{3}$ which can be written as $z^{5}y^{3}$

Report an Error

Example Question #112 : Polynomials

Simplify:

(x^2)(x^4)

Possible Answers:

x^8

x^6

x^2

$x^{-2}$

Correct answer:

x^6

Explanation:

When you multiply exponents with the same base, you add the exponents:

(x^2)(x^4)=x^6

Report an Error

Example Question #113 : Polynomials

Simplify:

(y^5)(y^9)

Possible Answers:

$y^{45}$

$y^{-4}$

y^4

$y^{14}$

Correct answer:

$y^{14}$

Explanation:

When you multiply exponents with the same base, you add the exponents:

$(y^5)(y^9)=y^{14}$

Report an Error

Example Question #114 : Polynomials

Simplify:

$(z^6)(z^{-2})$

Possible Answers:

z^4

$z^{-12}$

$z^{-4}$

z^8

Correct answer:

z^4

Explanation:

When you multiply exponents with the same base, you add the exponents:

$(z^6)(z^{-2})=z^{4}$

Report an Error

View Pre-Algebra Tutors

Nate
Certified Tutor

University of Wisconsin-Oshkosh, non degree, Prepharmacy. University of Wisconsin-Madison, Pharmaceutical Chemist, Pharmacy.

View Pre-Algebra Tutors

Chelsea
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Physics. The University of Texas at Dallas, Master of Science, Bioinf...

View Pre-Algebra Tutors

Ataul
Certified Tutor

Temple University, Bachelor of Science, Financial Planning.

All Pre-Algebra Resources

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

Popular Subjects

GRE Tutors in Denver, Reading Tutors in San Diego, Algebra Tutors in Houston, Computer Science Tutors in Denver, SAT Tutors in New York City, Computer Science Tutors in San Francisco-Bay Area, Statistics Tutors in San Diego, SSAT Tutors in Dallas Fort Worth, GRE Tutors in Los Angeles, Physics Tutors in New York City

Popular Courses & Classes

SSAT Courses & Classes in Seattle, LSAT Courses & Classes in Chicago, MCAT Courses & Classes in Los Angeles, GRE Courses & Classes in Washington DC, ACT Courses & Classes in Denver, GMAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Denver, LSAT Courses & Classes in Los Angeles, ACT Courses & Classes in Philadelphia, MCAT Courses & Classes in Chicago

Popular Test Prep

GRE Test Prep in Atlanta, GRE Test Prep in Miami, GMAT Test Prep in Dallas Fort Worth, SSAT Test Prep in San Francisco-Bay Area, GRE Test Prep in Dallas Fort Worth, LSAT Test Prep in Miami, MCAT Test Prep in New York City, LSAT Test Prep in San Diego, LSAT Test Prep in Atlanta, ISEE Test Prep in Phoenix

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 #11 : Product Rule Of Exponents

Example Question #12 : Product Rule Of Exponents

Example Question #13 : Product Rule Of Exponents

Example Question #13 : Product Rule Of Exponents

Example Question #111 : Polynomials

Example Question #16 : Product Rule Of Exponents

Example Question #112 : Polynomials

Example Question #112 : Polynomials

Example Question #113 : Polynomials

Example Question #114 : Polynomials

All Pre-Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: