Call Now to Set Up Tutoring:

(888) 888-0446

College Algebra : Integer Exponents

Study concepts, example questions & explanations for College Algebra

Create An Account

All College Algebra Resources

5 Diagnostic Tests 84 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Simplifying Exponents

Simplify the expression:

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

Possible Answers:

Cannot be simplified

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

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

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

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 #281 : College Algebra

Simplify:

(4x^3)^4

Possible Answers:

512x

$256x^{12}$

4x^7

$4x^{12}$

16x^7

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 #12 : Distributing Exponents (Power Rule)

Simplify the following expression:

(9x^6y^2z^5)^2

Possible Answers:

$81x^{12}y^4z^{10}$

$18x^{12}y^4z^{10}$

$11x^{12}y^4z^{10}$

$81x^{8}y^4z^{7}$

Correct answer:

$81x^{12}y^4z^{10}$

Explanation:

Simplify the following expression:

(9x^6y^2z^5)^2

To raise exponents to another power, we need to multiply them:

$(9x^6y^2z^5)^2=9^2x^{6*2}y^{2*2}z^{5*2}=81x^{12}y^4z^{10}$

So we get:

$81x^{12}y^4z^{10}$

Report an Error

Example Question #11 : Distributing Exponents (Power Rule)

Simplify.

$(x^4)^{6}$

Possible Answers:

$x^{-2}$

$x^{10}$

x^2

$x^{46}$

$x^{24}$

Correct answer:

$x^{24}$

Explanation:

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

$(x^4)^{6}=x^{4*6}=x^{24}$

Report an Error

Example Question #21 : Distributing Exponents (Power Rule)

Simplify.

$(\frac{x^5}{y^3})^3$

Possible Answers:

$\frac{x^{15}}{y^9}$

$\frac{x^{15}}{y^8}$

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

$\frac{x^{15}}{y^3}$

$\frac{x^{15}}{y^{13}}$

Correct answer:

$\frac{x^{15}}{y^9}$

Explanation:

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

$(\frac{x^5}{y^3})^{3}=\frac{x^{5*3}}{y^{3*3}}=\frac{x^{15}}{y^{9}}$

Report an Error

Example Question #3 : Review And Other Topics

Combine the following terms:

5x^4*3t^3*8x^3

Possible Answers:

16x^7t^3

120x^7t^3

$120x^{36}$

$120x^{10}$

Correct answer:

120x^7t^3

Explanation:

Combine the following terms:

5x^4*3t^3*8x^3

We need to multiply three terms together. We should recognize that the t must be left alone, because it cannot be combined with the x's.

First, multiply all three coefficients

5*3*8=120

Next, combine the x's. Because we are multiplying, we will add the exponents.

x^4*x^3=x^7

Now, put it all together to get:

120x^7t^3

Report an Error

Example Question #1 : Integer Exponents

Evaluate

X^7/X^4

Possible Answers:

$X^{28}$

$X^{7/4}$

X^3

7/4X

$X^{-3}$

Correct answer:

X^3

Explanation:

When common variables with exponents are divided, the exponents are subtracted.

$X^7/X^4 = X^{7-4} = X^3$

Report an Error

Example Question #283 : College Algebra

Evaluate

X^8*X^6

Possible Answers:

$X^{48}$

14X

48X

$X^{2}$

$X^{14}$

Correct answer:

$X^{14}$

Explanation:

When like terms with exponents are multiplied, you add the exponents.

$X^8*X^6 = X^{8+6} = X^{14}$

Report an Error

Example Question #282 : College Algebra

Evaluate the following:

$x^{2}*x^{4}=$

Possible Answers:

$x^{6}$

$x^{2}$

$x^{8}$

$2x^{4}$

Correct answer:

$x^{6}$

Explanation:

When similar terms raised to n are multiplied, simply add the exponents. Thus

$x^{2}*x^{4}=x^{2+4}=x^{6}$

Report an Error

Example Question #2 : Review And Other Topics

$x^{3}*x^{5}=$

Possible Answers:

$x^{15}$

$x^{2}$

15x

$x^{8}$

$x^{5}$

Correct answer:

$x^{8}$

Explanation:

When similar terms raised to n are multiplied, simply add the exponents. Thus

$x^{3}*x^{5}=x^{3+5}=x^{8}$

Report an Error

View College Algebra Tutors

Danielle
Certified Tutor

View College Algebra Tutors

Jethro
Certified Tutor

Federal University of Agriculture Abeokuta,, Bachelor of Engineering, Mechatronics, Robotics, and Automation Engineering.

View College Algebra Tutors

Blossom
Certified Tutor

University of Maryland-Baltimore County, Bachelor of Science, Computer Science.

All College Algebra Resources

5 Diagnostic Tests 84 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

GMAT Tutors in Washington DC, Computer Science Tutors in Washington DC, SAT Tutors in Denver, Chemistry Tutors in Chicago, Math Tutors in Houston, Physics Tutors in San Francisco-Bay Area, SSAT Tutors in Phoenix, Biology Tutors in Chicago, Physics Tutors in Dallas Fort Worth, SSAT Tutors in Dallas Fort Worth

Popular Courses & Classes

Spanish Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Philadelphia, SAT Courses & Classes in Houston, MCAT Courses & Classes in Denver, MCAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Philadelphia, GMAT Courses & Classes in Phoenix, SSAT Courses & Classes in Boston, ACT Courses & Classes in Chicago, SSAT Courses & Classes in Houston

Popular Test Prep

SAT Test Prep in Seattle, LSAT Test Prep in Los Angeles, GMAT Test Prep in San Diego, LSAT Test Prep in Houston, ISEE Test Prep in San Francisco-Bay Area, LSAT Test Prep in Phoenix, ISEE Test Prep in New York City, LSAT Test Prep in Philadelphia, SSAT Test Prep in Chicago, GMAT Test Prep in Houston

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

College Algebra : Integer Exponents

Study concepts, example questions & explanations for College Algebra

All College Algebra Resources

Example Questions

Example Question #1 : Simplifying Exponents

Example Question #281 : College Algebra

Example Question #12 : Distributing Exponents (Power Rule)

Example Question #11 : Distributing Exponents (Power Rule)

Example Question #21 : Distributing Exponents (Power Rule)

Example Question #3 : Review And Other Topics

Example Question #1 : Integer Exponents

Example Question #283 : College Algebra

Example Question #282 : College Algebra

Example Question #2 : Review And Other Topics

All College Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: