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 #31 : Product Rule Of Exponents

Simplify: $4^2 \cdot 4^{-5} \cdot 4^{10}$

Possible Answers:

4^7

$4^{-7}$

$4^{-4}$

4^4

$4^{-3}$

Correct answer:

4^7

Explanation:

Since the bases are all alike and are multiplied, the exponents can be added.

In mathematical terms:

$a^n\cdot a^m=a^{n+m}$

Plugging in four as our base and the various exponents we get the following,

$4^2 \cdot 4^{-5} \cdot 4^{10} = 4^{2-5+10} = 4^7$ .

Report an Error

Example Question #32 : Product Rule Of Exponents

Expand: (3x^3)^3

Possible Answers:

27 x^6

3x^9

9x^9

3x^6

27 x^9

Correct answer:

27 x^9

Explanation:

The exponents can be multiplied in this case.

Expand out the terms to verify.

(3x^3)^3 = (3x^3)(3x^3)(3x^3) = 27 x^9

Report an Error

Example Question #33 : Product Rule Of Exponents

Solve: 3(a^2)^3 + (3a^2)^3

Possible Answers:

27a^6

12a^6

30a^6

6a^6

9a^6

Correct answer:

30a^6

Explanation:

Evaluate the quantities inside the parentheses first. The powers are multiplied when they are bounded in the parentheses.

3(a^2)^3 + (3a^2)^3 = 3a^6 + 3^3(a^6)

3a^6 + 3^3(a^6) = 3a^6 + 27a^6

Combine like-terms.

3a^6 + 27a^6 = 30a^6

Report an Error

Example Question #130 : Polynomials

Evaluate:

$(a^2)^4\cdot(a^{-2})^3$

Possible Answers:

$a^{24}$

$\frac{1}{a^2}$

a^2

Correct answer:

a^2

Explanation:

Simplify each parentheses before multiplying.

Recall the rules of exponents which states if exponents are being raised to another one they are multiplied and if like bases are being multiplied their exponents are added.

$(a^n)^m=a^{n\cdot m}$

$a^n\cdot a^m=a^{n+m}$

Applying these rules we get,

$(a^2)^4\cdot(a^{-2})^3 = a^8 \cdot a^{-6} = a^{8+(-6)}=a^2$ .

Report an Error

Example Question #33 : Product Rule Of Exponents

Simplify: -b(b^2)^3

Possible Answers:

b^5-b

-b^6

-b^7

b^7-b

b^6-b

Correct answer:

-b^7

Explanation:

Evaluate the powers by multiplication.

-b(b^2)^3 = -b (b^6)

Use the power rule to combine the terms. The exponents can then be added.

-b (b^6) = -b^7

Report an Error

Example Question #35 : Product Rule Of Exponents

Solve: $(x^3)^2 \cdot (x^2)^3$

Possible Answers:

$x^{12}$

2x^5

$x^{10}$

$x^{25}$

2x^6

Correct answer:

$x^{12}$

Explanation:

Simplify the first two terms using the product rule of exponents. When the base of some power is squared, we can simply multiply the two powers together.

$(x^3)^2 \cdot (x^2)^3 = x^{3\times 2} \cdot x^{2\times 3}$

Simplify the powers.

$x^{3\times 2} \cdot x^{2\times 3} =x^6 \cdot x^6$

Use the power rule to add the powers since the bases are alike.

$x^6 \cdot x^6 = x^{6+6} = x^{12}$

Report an Error

Example Question #36 : Product Rule Of Exponents

Solve

(5x^2)(-3x^4)

Possible Answers:

-15x^6

2x^8

15x^6

2x^6

-15x^8

Correct answer:

-15x^6

Explanation:

If a variable has an exponent with the value of a, it means we are taking that variable and mulitplying it by itself a times. For example,

x^2 = x*x

x^3 = x*x*x

and so on.

So when we multiply

(5x^2)(-3x^4)

we can expand it to look like

(5*x*x)(-3*x*x*x*x)

If we multiply, we get

-15*x*x*x*x*x*x

which equals

-15x^6

Report an Error

Example Question #34 : Product Rule Of Exponents

Simplify the following:

$x^5 \cdot x^2$

Possible Answers:

$x^{10}$

x^3

x^7

x^2

$x^{52}$

Correct answer:

x^7

Explanation:

When you multiply two terms together with the same base, you add the exponents. So,

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

Report an Error

Example Question #38 : Product Rule Of Exponents

Simplify the following

$x^4 \cdot y^2 \cdot x^{-2} \cdot y$

Possible Answers:

$x^2 \cdot y^3$

$x^2 \cdot y^2$

$2x^2 \cdot 2y^3$

$x^{-8} \cdot y^2$

$x^6 \cdot y^2$

Correct answer:

$x^2 \cdot y^3$

Explanation:

When multiplying terms with the same base, we add the exponents. Therefore,

$x^4 \cdot y^2 \cdot x^{-2} \cdot y$

can be written as

$x^{4+ -2} \cdot y^{2 + 1}$

$x^2 \cdot y^3$

Report an Error

Example Question #35 : Product Rule Of Exponents

Simplify the following expression:

6x^3*8x^7

Possible Answers:

$48x^{10}$

$14x^{21}$

$14x^{10}$

$48x^{21}$

Correct answer:

$48x^{10}$

Explanation:

Simplify the following expression:

6x^3*8x^7

So, we are multiplying exponents. When doing so, we need to treat the numbers out in front like regular multiplication, and add the exponents:

$(6*8)x^{3+7}=48x^{10}$

So we have our answer:

$48x^{10}$

Report an Error

View Pre-Algebra Tutors

Arnav
Certified Tutor

Rutgers University-Newark, Bachelor of Science, Biomedical Engineering.

View Pre-Algebra Tutors

Soung
Certified Tutor

University of Chicago, Bachelor in Arts, Chemistry. Northwestern University, Doctor of Science, Molecular Pharmacology.

View Pre-Algebra Tutors

Nicholas
Certified Tutor

University of Minnesota-Twin Cities, Bachelor of Science, Chemical Engineering.

All Pre-Algebra Resources

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

Popular Subjects

GRE Tutors in Chicago, Calculus Tutors in Washington DC, Reading Tutors in Washington DC, Computer Science Tutors in San Francisco-Bay Area, Statistics Tutors in Miami, English Tutors in Dallas Fort Worth, LSAT Tutors in New York City, Computer Science Tutors in Denver, Reading Tutors in Los Angeles, SAT Tutors in New York City

Popular Courses & Classes

ISEE Courses & Classes in Los Angeles, SAT Courses & Classes in Houston, ACT Courses & Classes in Miami, SAT Courses & Classes in Denver, Spanish Courses & Classes in Seattle, ACT Courses & Classes in San Diego, GMAT Courses & Classes in Washington DC, LSAT Courses & Classes in Denver, MCAT Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Atlanta

Popular Test Prep

ACT Test Prep in San Diego, GRE Test Prep in Los Angeles, SSAT Test Prep in New York City, ISEE Test Prep in San Diego, GRE Test Prep in Houston, ACT Test Prep in Seattle, LSAT Test Prep in Phoenix, SAT Test Prep in Boston, SAT Test Prep in Houston, SAT Test Prep in Denver

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 #31 : Product Rule Of Exponents

Example Question #32 : Product Rule Of Exponents

Example Question #33 : Product Rule Of Exponents

Example Question #130 : Polynomials

Example Question #33 : Product Rule Of Exponents

Example Question #35 : Product Rule Of Exponents

Example Question #36 : Product Rule Of Exponents

Example Question #34 : Product Rule Of Exponents

Example Question #38 : Product Rule Of Exponents

Example Question #35 : 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: