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

← Previous 1 2 3 4 5 6 7 8 9 10 11 12 13 Next →

Example Question #61 : Distributing Exponents (Power Rule)

Simplify: $(4^{10})^{-3}$

Possible Answers:

$4^{-30}$

$16^{-3}$

$8^{30}$

4^7

$4^{-13}$

Correct answer:

$4^{-30}$

Explanation:

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

$(4^{10})^{-3}=4^{10*-3}=4^{-30}$

Report an Error

Example Question #61 : Distributing Exponents (Power Rule)

Simplify:

(a^3b^3)^2(a^2b^2)^3

Possible Answers:

$a^{4}b^{4}$

None of these

$a^{12}b^{12}$

$a^{10}b^{10}$

$a^{6}b^{6}$

Correct answer:

$a^{12}b^{12}$

Explanation:

Exponents outside of a parentheses are distributed through multiplication:

(a^3b^3)^2

becomes

a^6b^6

(a^2b^2)^3

becomes

a^6b^6

$a^6b^6*a^6b^6=a^{12}b^{12}$

Report an Error

Example Question #62 : Distributing Exponents (Power Rule)

Simplify:

$(5^{-8})^{-12}$

Possible Answers:

$5^{-96}$

$5^{-20}$

$25^{-20}$

25^8

$5^{96}$

Correct answer:

$5^{96}$

Explanation:

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

$(5^{-8})^{-12}=5^{-8*-12}=5^{96}$

Report an Error

Example Question #251 : Simplifying Exponents

Expand and simplify: [1+(2^2)^3]^2

Possible Answers:

531441

1089

4225

4096

4097

Correct answer:

4225

Explanation:

Evaluate the exponential term inside the bracket first. Use the product rule for exponents to simplify.

$(2^2)^3 = (2^2)(2^2)(2^2) = 2^{2\cdot 3} = 2^6 = 64$

The term inside the bracket becomes:

[1+64]^2

Simplify the term inside.

65^2 = 4225

The answer is: 4225

Report an Error

Example Question #252 : Simplifying Exponents

Solve: $(4^{150})^{5}$

Possible Answers:

$1024^{155}$

$4^{180}$

$4^{750}$

$4^{155}$

$1024^{30}$

Correct answer:

$4^{750}$

Explanation:

When the quantity of the terms of a base raised to a power is also raised to a power, we can use the product rule for exponents to expand this expression.

$(X^Y)^Z = X^{YZ}$

Multiply the powers together.

$(4^{150})^{5} = 4^{150\cdot 5} = 4^{750}$

The answer is: $4^{750}$

Report an Error

Example Question #63 : Distributing Exponents (Power Rule)

Simplify: (8x^3)^2

Possible Answers:

16x^6

8x^6

64x^6

16x^5

Correct answer:

64x^6

Explanation:

$When\ raising\ a\ power\ to\ a\ power\ multiply\ the\ exponents.$

(8x^3)^2=8^2x^(^3^*^2^)=64x^6

Report an Error

Example Question #254 : Simplifying Exponents

Simplify the exponents: $(2^3)^{-2}+(4^0)^3$

Possible Answers:

$\frac{1}{2}$

$\frac{65}{64}$

$\frac{13}{12}$

128

Correct answer:

$\frac{65}{64}$

Explanation:

To simplify this expression, since the powers are outside of a quantity of a power, we can multiply the powers together according to the power rule.

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

Simplify the expression.

$(2^3)^{-2}+(4^0)^3 = 2^{-6}+4^0$

Change the negative exponent into a fraction and simplify.

$2^{-6}+4^0 = \frac{1}{2^6}+1 = \frac{1}{64}+\frac{64}{64}$

The answer is: $\frac{65}{64}$

Report an Error

Example Question #255 : Simplifying Exponents

Simplify: $(\frac{1}{3^3})^{-2}$

Possible Answers:

243

$\frac{1}{243}$

$\frac{1}{3}$

$\frac{1}{729}$

729

Correct answer:

729

Explanation:

The fraction inside the parentheses can be rewritten as a negative exponent.

$(\frac{1}{3^3})^{-2}=(3^{-3})^{-2}$

Using the power property of exponents, multiply both exponents together.

$(3^{-3})^{-2} = 3^6$

Simplify this value.

$3^6 = 3\cdot3\cdot3\cdot3\cdot3\cdot3 = 729$

The answer is: 729

Report an Error

Example Question #256 : Simplifying Exponents

Simplify: $(3^{11}\cdot 3^{10})^3$

Possible Answers:

$3^{24}$

$3^{330}$

$3^{63}$

$3^{113}$

$9^{330}$

Correct answer:

$3^{63}$

Explanation:

Determine the inner term by using the additive rule of exponents. When the bases of a certain power are similar, the powers can be added.

$(3^{11}\cdot 3^{10})^3 =(3^{11+10})^3 = (3^{21})^3$

Use the power rule to simplify this term.

$(3^{21})^3 = 3^{21\times 3} = 3^{63}$

The answer is: $3^{63}$

Report an Error

Example Question #64 : Distributing Exponents (Power Rule)

Simplify: $(2x^{55})^{2}$

Possible Answers:

$2x^{57}$

$4x^{110}$

$2x^{110}$

$2x^{107}$

$4x^{57}$

Correct answer:

$4x^{110}$

Explanation:

According to the rule of exponents, we can distribute the power of two by multiplying the powers.

$(2x^{55})^{2} = (2x^{55})(2x^{55}) = (2^{1\times 2}x^{55 \times 2})$

Simplify the terms.

The answer is: $4x^{110}$

Report an Error

← Previous 1 2 3 4 5 6 7 8 9 10 11 12 13 Next →

View Algebra 2 Tutors

Gary
Certified Tutor

Montana State University, Bachelor of Science, Mathematics Teacher Education. Western Carolina University, Master of Arts, Ma...

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

Venkata Naga Sreelalitapriya
Certified Tutor

University of Central Florida, Bachelor of Science, Biotechnology.

All Algebra II Resources

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

Popular Subjects

English Tutors in San Diego, ISEE Tutors in Phoenix, French Tutors in Phoenix, MCAT Tutors in Phoenix, SSAT Tutors in Washington DC, Chemistry Tutors in Seattle, Biology Tutors in Miami, English Tutors in Phoenix, LSAT Tutors in Boston, Statistics Tutors in Chicago

Popular Courses & Classes

LSAT Courses & Classes in New York City, LSAT Courses & Classes in Atlanta, MCAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Houston, GMAT Courses & Classes in Atlanta, MCAT Courses & Classes in Los Angeles, SSAT Courses & Classes in Atlanta, ISEE Courses & Classes in Phoenix, SSAT Courses & Classes in Boston

Popular Test Prep

MCAT Test Prep in Miami, GRE Test Prep in Washington DC, LSAT Test Prep in Denver, GRE Test Prep in Seattle, SSAT Test Prep in Chicago, LSAT Test Prep in Atlanta, GMAT Test Prep in Atlanta, GMAT Test Prep in New York City, ISEE Test Prep in Denver, MCAT Test Prep in Washington DC

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 #61 : Distributing Exponents (Power Rule)

Example Question #61 : Distributing Exponents (Power Rule)

Example Question #62 : Distributing Exponents (Power Rule)

Example Question #251 : Simplifying Exponents

Example Question #252 : Simplifying Exponents

Example Question #63 : Distributing Exponents (Power Rule)

Example Question #254 : Simplifying Exponents

Example Question #255 : Simplifying Exponents

Example Question #256 : Simplifying Exponents

Example Question #64 : Distributing Exponents (Power Rule)

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: