We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Pre-Algebra : Power 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 : Power Rule Of Exponents

Simplify:

$\left ( 3x^{2}y \right )^{3}$

Possible Answers:

$9x^{2}y$

$27x^{6}y^{3}$

$3x^{5}y^{3}$

$9x^{6}y^{3}$

$3x^{2}y^{3}$

Correct answer:

$27x^{6}y^{3}$

Explanation:

Recall the Power Rule of Exponents: $\left ( x^{m} \right )^{n}=x^{m*n}$ .

To simplify the expression $\left ( 3x^{2}y \right )^{3}$ , use this rule to distribute the exponents:

$\left ( 3x^{2}y \right )^{3}=3^{3}x^{2*3}y^{3}=27x^{6}y^{3}$

Report an Error

Example Question #2 : Power Rule Of Exponents

Simplify:

$x^{5}\left ( x^{2}y \right )^{2}$

Possible Answers:

$x^{12}y^{2}$

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

$x^{20}y^{2}$

$x^{9}y^{2}$

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

Correct answer:

$x^{9}y^{2}$

Explanation:

Recall the following rules:

The Product Rule of Exponents says: $x^{m}*x^{n}=x^{m+n}$

The Power Rule of Exponents says: $\left ( x^{m} \right )^{n}=x^{m*n}$ and $\left ( x^{m}y \right )^{n}=x^{m*n}y^{n}$

Step 1: Use the Power Rule of Exponents to distribute the exponents:

$\left ( x^{2}y \right )^{2}=x^{2*2}y^{2}=x^{4}y^{2}$

Step 2: Use the Product Rule of Exponents to simplify further:

$x^{5}x^{4}y^{2}=x^{5+4}y^{2}=x^{9}y^{2}$

Report an Error

Example Question #3 : Power Rule Of Exponents

Simplify.

$\frac{x^{8}}{x^{6}}$

Possible Answers:

$x^{14}$

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

$x^{2}$

$x^{-2}$

Correct answer:

$x^{2}$

Explanation:

The Quotient of Powers Property states when you divide two powers with the same base, you subtract the exponents.

In this case, the exponents are 8 and 6:

$x^{8-6}=x^{2}$

Report an Error

Example Question #2 : Power Rule Of Exponents

Simplify:

$\small \small (4xy^3z^2)^2$

Possible Answers:

$\small \small 16x^2y^6z^4$

$\small 8x^2y^6z^4$

$\small 16x^3y^5z^4$

$\small \small 8x^3y^5z^4$

Correct answer:

$\small \small 16x^2y^6z^4$

Explanation:

Recall, to distribute exponents through a polynomial, you must multiply the exponents. Thus, our expression can be simplified as follows:

$\small \small (4xy^3z^2)^2$

$\small 4^{1*2}x^{1*2}y^{3*2}z^{2*2}$

$\small 4^2x^2y^6z^4$

$\small 16x^2y^6z^4$

Report an Error

Example Question #1 : Power Rule Of Exponents

Simplify:

x^4y(x^3y^2)^2

Possible Answers:

$x^{24}y^4$

$x^{7}y^5$

$x^{10}y^5$

$4x^{10}y^5$

$x^{9}y^4$

Correct answer:

$x^{10}y^5$

Explanation:

Recall the following rules:

The Product Rule of Exponents says: $x^m * x^n = x^{m+n}$

The Power Rule of Exponents says: $(x^m)^n = x^{m+n}$ and $(x^my)^n = x^{m*n}y^n$

Step 1: Use the Power Rule of Exponents to distribute the exponents:

$(x^3y^2)^2 = x^{3*2}y^{2*2} = x^6y^4$

Step 2: Use the Product Rule of Exponents to simplify further:

$x^4y(x^6y^4) = x^{4+6}y^{1+4} = x^{10}y^5$

Report an Error

Example Question #4 : Power Rule Of Exponents

Simplify:

$(5x^{2}y^{^{3}})^{2}$

Possible Answers:

$25x^{2}y^{6}$

$25x^{4}y^{5}$

$10x^{4}y^{6}$

$25x^{4}y^{6}$

$125x^{4}y^{6}$

Correct answer:

$25x^{4}y^{6}$

Explanation:

Recall the Power Rule of Exponents: $(x^{m})^{n}= x^{m*n}$

To simplify the expression $(5x^{2}y^{^{3}})^{2}$ , use this rule to distribute the exponents:

$(5x^{2}y^{^{3}})^{2} = 5^{2}x^{2*2}y^{3*2} = 25x^{4}y^{6}$

Report an Error

Example Question #7 : Power Rule Of Exponents

y(2x^2y^3)^2

Possible Answers:

4x^4y^6

2x^4y^7

4x^4y^5

4x^4y^8

4x^4y^7

Correct answer:

4x^4y^7

Explanation:

First, distribute the exponent outside of the parentheses to each of the elements inside of the parentheses, including the 2.

(2x^2y^3)^2 = 2^2x^4y^6

Remember that in this case, when an exponent is raised to another power, the exponents multiply.

Now we need to mutiply that answer by the outside .

4x^4y^6*y = 4x^4y^7

For this last step, remember that the exponents on the add.

Report an Error

Example Question #2 : Power Rule Of Exponents

What is the simplified version of the following polynomial?

$\small x^{24}* x^2 + 2^2 + 2^2$

Possible Answers:

$\small 8\small x^{26}$

$\small \small x^{26}+16$

$\small \small x^{48}+8$

$\small \small 8x^{48}$

$\small x^{26}+8$

Correct answer:

$\small x^{26}+8$

Explanation:

The power rule of an exponent means that when two exponential expressions with the same base are multiplied, you add the exponents together. In this case,

$\small \small \small \small x^{24}*x^2 = x^{26}$

$\small x^{24}$ can be thought of as a "string" of 24 $\small x$ variables being multiplied together, so by multiplying that string by another 2 variable units, you have seamlessly extended the chain by two units.

For $\small 2^2 +2^2$ , it is important to remember that the power rule does no apply during addition, so the exponent is applied first, then the exponential values are added following the order of operation, so the final expression is:

$\small \small x^{24 +2} + 4+4$

or $\small x^{26} + 8$

Report an Error

Example Question #2 : Power Rule Of Exponents

Simplify:
(x^5)(x^8)

Possible Answers:

x^3

$x^{\frac{5}{8}}$

$x^{13}$

$x^{40}$

Correct answer:

$x^{13}$

Explanation:

The product rule of exponents states that when you're multiplying two powers with the same base, you add the exponents:

$(x^a)(x^b)=x^{a+b}$

In this instance,

$(x^5)(x^8)=x^{5+8}=x^{13}$

Report an Error

Example Question #61 : Polynomials

Simplify:
$\small (x^3)^4$

Possible Answers:

$\small x^1$

$\small x^{\frac{3}{4}}$

$\small \small x^7$

$\small x^{12}$

Correct answer:

$\small x^{12}$

Explanation:

The "power rule" states that when you raise a power to a power, you mutiploy the exponents:
$\small (x^a)^b=x^{a\times b}$

$\small (x^3)^4=x^{3\times4}=x^{12}$

Report an Error

View Pre-Algebra Tutors

James
Certified Tutor

University of Georgia, Bachelor in Arts, Political Science and Government.

View Pre-Algebra Tutors

Saarim
Certified Tutor

St Edwards University, Bachelor of Science, Mathematics.

View Pre-Algebra Tutors

Molly
Certified Tutor

Cornell University, Bachelor of Science, Biological and Physical Sciences. Cornell University, Bachelor of Science, Biochemis...

All Pre-Algebra Resources

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

Popular Subjects

LSAT Tutors in Philadelphia, ACT Tutors in Houston, GRE Tutors in Chicago, English Tutors in San Francisco-Bay Area, Physics Tutors in Los Angeles, Chemistry Tutors in Houston, English Tutors in San Diego, SSAT Tutors in Houston, French Tutors in San Diego, Math Tutors in Los Angeles

Popular Courses & Classes

ISEE Courses & Classes in Phoenix, SAT Courses & Classes in Chicago, ACT Courses & Classes in Boston, SAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Chicago, ACT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Houston, GMAT Courses & Classes in Miami, ACT Courses & Classes in Miami, SSAT Courses & Classes in Los Angeles

Popular Test Prep

SAT Test Prep in Denver, SSAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Phoenix, SSAT Test Prep in Dallas Fort Worth, ACT Test Prep in Philadelphia, GRE Test Prep in Chicago, SAT Test Prep in Boston, ACT Test Prep in New York City, MCAT Test Prep in Dallas Fort Worth, LSAT Test Prep in Atlanta

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 : Power Rule of Exponents

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #1 : Power Rule Of Exponents

Example Question #2 : Power Rule Of Exponents

Example Question #3 : Power Rule Of Exponents

Example Question #2 : Power Rule Of Exponents

Example Question #1 : Power Rule Of Exponents

Example Question #4 : Power Rule Of Exponents

Example Question #7 : Power Rule Of Exponents

Example Question #2 : Power Rule Of Exponents

Example Question #2 : Power Rule Of Exponents

Example Question #61 : Polynomials

All Pre-Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: