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 #90 : Polynomials

Simplify the following

(a^4)^2

Possible Answers:

a^2

a^8

a^6

$a^{42}$

a^4

Correct answer:

a^8

Explanation:

When you have the same base and you raise a power to a power, you multiply the exponents. So,

$(a^4)^2 = a^{4 \cdot 2} = a^8$

Report an Error

Example Question #91 : Polynomials

Simplify the following:

(b^4)^9

Possible Answers:

$b^{36}$

b^9

$b^{13}$

b^5

$b^{49}$

Correct answer:

$b^{36}$

Explanation:

If you are raising a power to another power, you simply multiply the powers together. So,

$(b^4)^9 = b^{4 \cdot 9} = b^{36}$

Report an Error

Example Question #33 : Power Rule Of Exponents

Simplify the following:

$(a^3)^4 + (b^2)^{-5}$

Possible Answers:

$a^7 + b^{-3}$

$a^{12} + b^{-10}$

$a^7b^{-3}$

$a^{12}b^{-10}$

(ab)^2

Correct answer:

$a^{12} + b^{-10}$

Explanation:

When raising a power to a power, we multiply the exponents. In this case, we get

$(a^3)^4 + (b^2)^{-5}$

$a^{3 \cdot 4} + b^{2 \cdot -5}$

$a^{12} + b^{-10}$

And since they have different bases, we cannot combine them any further.

Report an Error

Example Question #92 : Polynomials

Which answer shows the answer to:

19^8 * 19^4 =

Possible Answers:

19^1^2

19^4

19^2

19^1^6

19^3^2

Correct answer:

19^1^2

Explanation:

19 is the base number. It is the same on both sides.

If the base is the same on both sides and it is a multiplication problem we keep the base and add the exponents together.

19^8 ^ + ^4

= 19^1^2

Report an Error

Example Question #35 : Power Rule Of Exponents

Simplify the following:

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

Possible Answers:

$x^{-6}y^{-12}$

$x^{-1} + y^{-7}$

$x^{-6} + y^{-12}$

$x^{-5}y$

$x^{-5} + y$

Correct answer:

$x^{-6} + y^{-12}$

Explanation:

The power rule for exponents states that when you raise a power to a power, you multiply the exponents, keeping the base the same. So,

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

can be written as

$x^{\ 2 \ \cdot \ -3} + y^{\ -3 \ \cdot \ 4}$

$x^{-6} + y^{-12}$

Since we cannot combine two different bases, this is now in simplest form.

Report an Error

Example Question #93 : Polynomials

Simplify the polynomial.

$(2m^{2}n^{4}y^{3})^{2}$

Possible Answers:

$4mny^{8}$

$4m^{4}n^{6}y^{5}$

$4mny^{18}$

$4m^{4}n^{8}y^{6}$

$4m^{2}n^{4}y^{3}$

Correct answer:

$4m^{4}n^{8}y^{6}$

Explanation:

In order to solve this problem you must take every integer and variable to the power of 2 like so,

$(2m^{2}n^{4}y^{3})^{2}= 2^{2}m^{2\cdot 2}n^{4\cdot 2}y^{3\cdot 2}=4m^{4}n^{8}y^{6}$

Report an Error

Example Question #94 : Polynomials

Simplify the following:

$({x^{9}})^6$ +(y^3)^4

Possible Answers:

$x^{{54}}+y^{12}$

$x^{{15}}+y^{7}$

$x^{{15}}+y^{12}$

$x^{{54}}+y^{7}$

None of the above

Correct answer:

$x^{{54}}+y^{12}$

Explanation:

When you raise an exponent to an additional power you need to multiply the two numbers, so you will get:

$x^{{9*6}}+y^{3*4}$ which equals $x^{{54}}+y^{12}$

Report an Error

View Pre-Algebra Tutors

Alex
Certified Tutor

Vanderbilt University, Bachelor of Science, Psychology. Boston University, Master of Science, Speech-Language Pathology.

View Pre-Algebra Tutors

Michelle
Certified Tutor

University of Rhode Island, Bachelor of Science, Marine Biology. University of Rhode Island, Master of Arts, High School Teac...

View Pre-Algebra Tutors

Joy
Certified Tutor

Boston University, Bachelor in Arts, Conservation Biology.

All Pre-Algebra Resources

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

Popular Subjects

Spanish Tutors in Houston, Biology Tutors in Dallas Fort Worth, ACT Tutors in Dallas Fort Worth, Chemistry Tutors in Chicago, ISEE Tutors in Washington DC, SAT Tutors in New York City, Reading Tutors in Denver, Calculus Tutors in Chicago, MCAT Tutors in New York City, ISEE Tutors in Seattle

Popular Courses & Classes

SAT Courses & Classes in Miami, GRE Courses & Classes in Chicago, LSAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Boston, GRE Courses & Classes in Seattle, ACT Courses & Classes in Miami, Spanish Courses & Classes in Miami, SSAT Courses & Classes in Phoenix, ISEE Courses & Classes in Denver, ISEE Courses & Classes in Washington DC

Popular Test Prep

ISEE Test Prep in Washington DC, SSAT Test Prep in New York City, SAT Test Prep in Atlanta, LSAT Test Prep in Chicago, SSAT Test Prep in San Diego, ACT Test Prep in Seattle, SSAT Test Prep in Boston, SSAT Test Prep in Phoenix, ACT Test Prep in Dallas Fort Worth, ISEE Test Prep in Philadelphia

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 #90 : Polynomials

Example Question #91 : Polynomials

Example Question #33 : Power Rule Of Exponents

Example Question #92 : Polynomials

Example Question #35 : Power Rule Of Exponents

Example Question #93 : Polynomials

Example Question #94 : Polynomials

All Pre-Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: