We are open Saturday and Sunday!

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 #1 : Distributing Exponents (Power Rule)

What is the largest positive integer, , such that 2^z is a factor of 16^4 ?

Possible Answers:

Correct answer:

Explanation:

16^4 = (2^4)^4 = 2^1^6 . Thus, is equal to 16.

Report an Error

Example Question #1 : Simplifying Exponents

Simplify the expression:

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

Possible Answers:

$\frac{3x}{16y^3}$

$\frac{3x}{64y^3}$

$\frac{3x}{64y^4}$

Cannot be simplified

Correct answer:

$\frac{3x}{64y^4}$

Explanation:

Begin by distributing the exponent through the parentheses. The power rule dictates that an exponent raised to another exponent means that the two exponents are multiplied:

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

Any negative exponents can be converted to positive exponents in the denominator of a fraction:

$\frac{3x^4y^2}{64x^3y^6}$

The like terms can be simplified by subtracting the power of the denominator from the power of the numerator:

$\frac{3x^4y^2}{64x^3y^6}=\frac{3}{64}x^{4-3}y^{2-6}=\frac{3}{64}xy^{-4}$

$\frac{3x}{64y^4}$

Report an Error

Example Question #2 : Simplifying Exponents

Order the following from least to greatest:

$25^{100}$

$2^{300}$

$3^{500}$

$4^{400}$

$2^{600}$

Possible Answers:

$3^{500}, 4^{400}, 2^{300}, 25^{100}, 2^{600}$

$2^{300}, 2^{600}, 3^{500}, 25^{100}, 4^{400}$

$25^{100}, 2^{300}, 2^{600}, 3^{500}, 4^{400}$

$2^{300}, 25^{100}, 2^{600}, 3^{500}, 4^{400}$

$2^{600}, 2^{300}, 25^{100}, 3^{500}, 4^{400}$

Correct answer:

$2^{300}, 25^{100}, 2^{600}, 3^{500}, 4^{400}$

Explanation:

In order to solve this problem, each of the answer choices needs to be simplified.

Instead of simplifying completely, make all terms into a form such that they have 100 as the exponent. Then they can be easily compared.

2^3^0^0 = (2^3)^1^0^0 = 8^1^0^0 , 3^5^0^0 = (3^5)^1^0^0 = 243^1^0^0 , 4^4^0^0 = (4^4)^1^0^0 = 256^1^0^0 , and 2^6^0^0 = (2^6)^1^0^0 = 64^1^0^0 .

Thus, ordering from least to greatest: 8^1^0^0, 25^1^0^0, 64^1^0^0, 243^1^0^0, 256^1^0^0 .

Report an Error

Example Question #4 : Distributing Exponents (Power Rule)

Simplify:

$\frac{(x^{4})^{3}(5x)^{-5}}{xy}$

Possible Answers:

$\frac{125x^{2}}{y}$

$\frac{5x}{y}$

$\frac{x^{6}}{3125y}$

$\frac{1}{y}$

$\frac{x^{12}}{5y}$

Correct answer:

$\frac{x^{6}}{3125y}$

Explanation:

$\frac{(x^{4})^{3}(5x)^{-5}}{xy}$

Step 1: Distribute the exponents in the numberator.

$\frac{x^{12}5^{-5}x^{-5}}{xy}$

Step 2: Represent the negative exponents in the demoninator.

$\frac{x^{12}}{5^{5}x^{5}xy}$

Step 3: Simplify by combining terms.

$\frac{x^{12}}{3125x^{6}y}$

$\frac{x^6}{3125y}$

Report an Error

Example Question #1 : Distributing Exponents (Power Rule)

Simplify:

(4x^3)^4

Possible Answers:

16x^7

$256x^{12}$

4x^7

512x

$4x^{12}$

Correct answer:

$256x^{12}$

Explanation:

Use the power rule to distribute the exponent:

$(4x^3)^4\rightarrow 4^4\cdot x^{3\cdot 4}\rightarrow 256x^{12}$

Report an Error

Example Question #1 : Distributing Exponents (Power Rule)

Simplify:

$\left ( \frac{a^2b^{-4}}{a^3b^6c^{-7}} \right )^{-4}$

Possible Answers:

$\left ( \frac{ab}{c} \right )$

$\left ( \frac{c^{16}}{ab^4} \right )$

$\left ( \frac{a^{20}b^8}{c^{28}} \right )$

$\left ( \frac{a^4b^{40}}{c^{28}} \right )$

Correct answer:

$\left ( \frac{a^4b^{40}}{c^{28}} \right )$

Explanation:

Step 1: Distribute the exponent through the terms in parentheses:

$\left ( \frac{a^{-8}b^{16}}{a^{-12}b^{-24}c^{28}} \right )$

Step 2: Use the division of exponents rule. Subtract the exponents in the numerator from the exponents in the denominator:

${\color{Red} \left ( \frac{a^4b^{40}}{c^{28}} \right )}$

Report an Error

Example Question #1 : Distributing Exponents (Power Rule)

Simplify.

$({x^{2a}}{x^{-b}})^2$

Possible Answers:

$x^{4a+b}$

$\frac{x^{4a}}{x^{2b}}$

$\frac{x^{2a}}{x^{2b}}$

$\frac{x^{4a}}{x^b}$

$x^{4a^2-4ab+b2}$

Correct answer:

$\frac{x^{4a}}{x^{2b}}$

Explanation:

When a power applies to an exponent, it acts as a multiplier, so 2a becomes 4a and -b becomes -2b. The negative exponent is moved to the denominator.

Report an Error

Example Question #2 : Distributing Exponents (Power Rule)

Simplify (x^2y^4)^2 .

Possible Answers:

x^4y^8

xy^2

y^2

x^2y^2

x^4y^6

Correct answer:

x^4y^8

Explanation:

When faced with a problem that has an exponent raised to another exponent, the powers are multiplied: $x^{2\cdot2}y^{4\cdot2}$ then simplify: x^4y^8 .

Report an Error

Example Question #1 : Distributing Exponents (Power Rule)

Solve: -25^0-(5^2)^0

Possible Answers:

Correct answer:

Explanation:

Solve each term separately. A number to the zeroth power is equal to 1, but be careful to apply the signs after the terms have been simplified.

-25^0-(5^2)^0 = -1-1 =-2

Report an Error

Example Question #1 : Distributing Exponents (Power Rule)

Simplify this expression: $\left(8x^5x^3y^2\right)^2$

Possible Answers:

$16x^{34}y^4$

$64x^{16}y^4$

$64x^{30}y^4$

$64x^{34}y^4$

$16x^{12} y^4$

Correct answer:

$64x^{16}y^4$

Explanation:

$64x^{16}y^4$ is the correct answer because the order of operations were followed and the multiplication and power rules of exponents were obeyed. These rules are as follows: PEMDAS (parentheses,exponents, multiplication, division, addition, subtraction), for multiplication of exponents follow the format $a^m*a^n=a^{m+n}$ , and $(a^m)^n=a^{m*n}$ .

[8x^5x^3y^2]^2

First we simplify terms within the parenthesis because of the order of operations and the multiplication rule of exponents:

[8x^8y^2]^2

Next we use the power rule to distribute the outer power:

8^2(x^8)^2(y^2)^2 = $64x^{16}y^4$

**note that in the first step it isn't necessary to combine the two x powers because the individuals terms will still add to x^16 at the end if you use the power rule correctly. However, following the order of operations is a great way to avoid simple math errors and is relevant in many problems.

Report an Error

View Algebra 2 Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

View Algebra 2 Tutors

Nicholas
Certified Tutor

Fordham University, Bachelors, Business Administration and Management. Boston University, Masters, Media Ventures.

View Algebra 2 Tutors

Gayathri
Certified Tutor

IISER Tirupati, Master of Science, Biology, General.

All Algebra II Resources

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

Popular Subjects

MCAT Tutors in Los Angeles, ACT Tutors in Boston, SAT Tutors in Dallas Fort Worth, GMAT Tutors in San Francisco-Bay Area, Calculus Tutors in San Diego, French Tutors in Philadelphia, Computer Science Tutors in New York City, English Tutors in Seattle, Math Tutors in Seattle, Algebra Tutors in Denver

Popular Courses & Classes

ISEE Courses & Classes in Houston, MCAT Courses & Classes in Atlanta, GRE Courses & Classes in Philadelphia, ACT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Phoenix, ACT Courses & Classes in Denver, ACT Courses & Classes in New York City, ISEE Courses & Classes in Denver, SSAT Courses & Classes in New York City, Spanish Courses & Classes in New York City

Popular Test Prep

LSAT Test Prep in Chicago, GRE Test Prep in Phoenix, ACT Test Prep in Houston, SSAT Test Prep in Dallas Fort Worth, ISEE Test Prep in New York City, ACT Test Prep in Denver, ACT Test Prep in San Francisco-Bay Area, GRE Test Prep in Los Angeles, GRE Test Prep in Houston, LSAT 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 #1 : Distributing Exponents (Power Rule)

Example Question #1 : Simplifying Exponents

Example Question #2 : Simplifying Exponents

Example Question #4 : Distributing Exponents (Power Rule)

Example Question #1 : Distributing Exponents (Power Rule)

Example Question #1 : Distributing Exponents (Power Rule)

Example Question #1 : Distributing Exponents (Power Rule)

Example Question #2 : Distributing Exponents (Power Rule)

Example Question #1 : Distributing Exponents (Power Rule)

Example Question #1 : 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: