Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Distributing Exponents (Power Rule)

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #31 : Distributing Exponents (Power Rule)

Simplify:

$(24^{12})^{\frac{1}{18}}$

Possible Answers:

$4\sqrt[3]{9}$

$9\sqrt[3]{4}$

$24\sqrt[3]{2}$

Correct answer:

$4\sqrt[3]{9}$

Explanation:

When exponents are being raised by another exponent, we just multiply the powers.

$(24^{12})^{\frac{1}{18}}=24^{12*\frac{1}{18}}=24^{\frac{2}{3}}$

When we have fractional exponents, we convert like this:

$x^{\frac{a}b{}}=\sqrt[b]{x^a}$ . is the index of the radical which is the denominator of the fractional exponent, is the power that will raise the base which is the numerator of the fractional exponent and is the base.

$24^{\frac{2}{3}}=\sqrt[3]{24^2}=\sqrt[3]{576}$ The perfect cube we can get is .

$\sqrt[3]{576}=\sqrt[3]{64*9}=4\sqrt[3]{9}$

Report an Error

Example Question #31 : Distributing Exponents (Power Rule)

Evaluate:

(2^9)^4

Possible Answers:

$2^{13}$

$4^{10}$

4^8

8^9

$2^{36}$

Correct answer:

$2^{36}$

Explanation:

When dealing exponents being raised by a power, we multiply the exponents and keep the base.

$(2^9)^4=2^{9*4}=2^{36}$

Report an Error

Example Question #32 : Distributing Exponents (Power Rule)

Evaluate:

$(5^{6})^7$

Possible Answers:

$5^{13}$

$5^{42}$

25^5

$5^{28}$

$5^{20}$

Correct answer:

$5^{42}$

Explanation:

When dealing exponents being raised by a power, we multiply the exponents and keep the base.

$(5^{6})^7=5^{6*7}=5^{42}$

Report an Error

Example Question #221 : Simplifying Exponents

Evaluate:

(9^9)^9

Possible Answers:

$9^{81}$

$81^{18}$

$81^{9}$

$9^{18}$

$9^{99}$

Correct answer:

$9^{81}$

Explanation:

When dealing with exponents being raised by another exponent, we multiply the powers and keep the base the same.

$(9^9)^9=9^{9*9}=9^{81}$

Report an Error

Example Question #222 : Simplifying Exponents

Evaluate:

$(3^{15})^7$

Possible Answers:

$9^{12}$

$9^{15}$

$3^{105}$

$3^{42}$

$3^{22}$

Correct answer:

$3^{105}$

Explanation:

When dealing with exponents being raised by another exponent, we multiply the powers and keep the base the same.

$(3^{15})^7=3^{15*7}=3^{105}$

Report an Error

Example Question #223 : Simplifying Exponents

Evaluate:

(18^5)^5

Possible Answers:

$18^{55}$

$90^{5}$

$90^{25}$

$18^{10}$

$18^{25}$

Correct answer:

$18^{25}$

Explanation:

When an exponent is raised by another power, we will multiply the exponents and keep the base the same.

Therefore:

$(18^5)^5=18^{5*5}=18^{25}$

Report an Error

Example Question #224 : Simplifying Exponents

Evaluate:

$\left(\left(\frac{1}{2}\right)^6\right)^{\frac{1}{2}}$

Possible Answers:

$\frac{1}{4}$

$\frac{1}{8}$

$\frac{1}{16}$

Correct answer:

$\frac{1}{8}$

Explanation:

When an exponent is raised by another power, we will multiply the exponents and keep the base the same.

Therefore:

$\left(\left(\frac{1}{2}\right)^6\right)^{\frac{1}{2}}=\left(\frac{1}{2}\right)^{6*\frac{1}{2}}=\frac{1}{2^{3}}=\frac{1}{8}$

Report an Error

Example Question #38 : Distributing Exponents (Power Rule)

Simplify:

(x+y)^2+(xy)^2

Possible Answers:

x^2+4xy+y^2

x^2+2xy+y^2+x^2y^2

2x^2+2y^2

x^2+y^2+x^2y^2

Correct answer:

x^2+2xy+y^2+x^2y^2

Explanation:

To start, we must examine the first term. Note that we are squaring a sum, so we cannot simply distribute the power of 2 to each term. We must take the sum times the sum:

(x+y)(x+y)=x^2+2xy+y^2

The second term, however, is a product, in which case we can distribute the power:

(xy)^2=x^2y^2

Adding the two together, we get

x^2+2xy+y^2+x^2y^2

Report an Error

Example Question #225 : Simplifying Exponents

Simplify: (2^5)^9

Possible Answers:

$2^{24}$

$2^{14}$

$2^{88}$

$2^{45}$

$2^{16}$

Correct answer:

$2^{45}$

Explanation:

When an exponent is raised by another exponent, we just multiply the exponents and keep the base the same.

$(2^5)^9=2^{5*9}=2^{45}$

Report an Error

Example Question #226 : Simplifying Exponents

Simplify: $(17^8)^{-4}$

Possible Answers:

$17^{-32}$

$17^{-12}$

17^4

$17^{-4}$

$17^{8}$

Correct answer:

$17^{-32}$

Explanation:

When an exponent is raised by another exponent, we just multiply the exponents and keep the base the same.

$(17^8)^{-4}=17^{8*-4}=17^{-32}$

Report an Error

View Algebra 2 Tutors

John
Certified Tutor

The University of Texas at Arlington, Bachelor of Science, Mathematics. Stanford University, Master of Science, Aerospace Eng...

View Algebra 2 Tutors

Nicholas
Certified Tutor

Salem State University, Bachelor of Science, GIS Technology.

View Algebra 2 Tutors

Sharon
Certified Tutor

Tabor College, Bachelor of Science, Mathematics Teacher Education. Tabor College, Masters in Education, Education.

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

English Tutors in Los Angeles, MCAT Tutors in Atlanta, Computer Science Tutors in Chicago, MCAT Tutors in San Diego, SSAT Tutors in Houston, LSAT Tutors in Los Angeles, GRE Tutors in Boston, Computer Science Tutors in San Francisco-Bay Area, ACT Tutors in Boston, Math Tutors in Chicago

Popular Courses & Classes

Spanish Courses & Classes in Houston, ISEE Courses & Classes in New York City, SSAT Courses & Classes in Atlanta, GMAT Courses & Classes in New York City, GMAT Courses & Classes in Boston, MCAT Courses & Classes in Houston, MCAT Courses & Classes in San Diego, ISEE Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Washington DC, GRE Courses & Classes in Phoenix

Popular Test Prep

ISEE Test Prep in Chicago, GMAT Test Prep in New York City, LSAT Test Prep in Chicago, SAT Test Prep in Dallas Fort Worth, SSAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Boston, SSAT Test Prep in Boston, ACT Test Prep in Seattle, MCAT Test Prep in Washington DC, GRE Test Prep in Boston

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

Algebra II : Distributing Exponents (Power Rule)

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #31 : Distributing Exponents (Power Rule)

Example Question #31 : Distributing Exponents (Power Rule)

Example Question #32 : Distributing Exponents (Power Rule)

Example Question #221 : Simplifying Exponents

Example Question #222 : Simplifying Exponents

Example Question #223 : Simplifying Exponents

Example Question #224 : Simplifying Exponents

Example Question #38 : Distributing Exponents (Power Rule)

Example Question #225 : Simplifying Exponents

Example Question #226 : Simplifying Exponents

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: