Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Exponents

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 #140 : Multiplying And Dividing Exponents

Simplify: $(\frac{x}{y})^4*(\frac{y^2}{x^{-3}})^2$

Possible Answers:

$x^{10}y^3$

$x^{10}$

$\frac{x}{y}$

$\frac{x^7}{y}$

$\frac{x^7}{y^3}$

Correct answer:

$x^{10}$

Explanation:

We apply the exponents first before simplifying the fractions.

$(\frac{x}{y})^4*(\frac{y^2}{x^{-3}})^2=\frac{x^4}{y^4}*\frac{y^4}{x^{-6}}$ The y^4 cancels and we have $\frac{x^4}{x^{-6}}$ . When dividing exponents, we subtract the exponents and keep the base the same.

$\frac{x^4}{x^{-6}}=x^{4-(-6)}=x^{10}$

Report an Error

Example Question #141 : Multiplying And Dividing Exponents

Simplify: $\frac{x^7}{x^8}$

Possible Answers:

$-\frac{1}{x}$

$\frac{1}{x}$

$x^{15}$

$\frac{1}{x^2}$

Correct answer:

$\frac{1}{x}$

Explanation:

When dividing exponents, we subtract the exponents and keep the base the same.

$\frac{x^7}{x^8}=x^{7-8}=x^{-1}$ We know with negative exponents, it's expressed as one over the positive exponent.

$x^{-1}=\frac{1}{x}$

Report an Error

Example Question #3602 : Algebra Ii

Simplify: $x^5*(\frac{5}{x^4})^2*\frac{x^8}{10}$

Possible Answers:

$\frac{5x^4}{2}$

$\frac{x^9}{2}$

x^5

$\frac{5x^9}{2}$

$\frac{5x^5}{2}$

Correct answer:

$\frac{5x^5}{2}$

Explanation:

Let's apply the exponents to the parentheses first and then simplify.

$x^5*(\frac{5}{x^4})^2*\frac{x^8}{10}=x^5*\frac{25}{x^8}*\frac{x^8}{10}$ The x^8 cancels and the numbers can be reduced by .

We finally get: $\frac{5x^5}{2}$ .

Report an Error

Example Question #142 : Multiplying And Dividing Exponents

Simplify and express as exponents: $\frac{x^4}{y^7}*x^{-8}$

Possible Answers:

(xy)^4

(xy)^7

$x^{-4}y^7$

$x^{-4}y^{-7}$

x^4y^7

Correct answer:

$x^{-4}y^{-7}$

Explanation:

Let's rewrite this as just exponents. Remember we can breakup $\frac{x^4}{y^7}=x^4*\frac{1}{y^7}$ . $\frac{x^4}{y^7}*x^{-8}=\frac{1}{y^7}*x^4*x^{-8}=y^{-7}*x^{-4}$

Report an Error

Example Question #143 : Multiplying And Dividing Exponents

Simplify: $\frac{5^{2x}}{5^{2x+4}}$

Possible Answers:

$\frac{1}{5^4}$

-5^4

5^4

$-\frac{1}{5^4}$

Correct answer:

$\frac{1}{5^4}$

Explanation:

When dividing exponents, we subtract the exponents and keep the base the same.

$\frac{5^{2x}}{5^{2x+4}}=5^{2x-(2x+4)}=5^{2x-2x-4}=5^{-4}=\frac{1}{5^4}$ We know with negative exponents, it's expressed as one over the positive exponent.

Report an Error

Example Question #144 : Multiplying And Dividing Exponents

Simplify: $\frac{7^{8x+4}}{7^{7x-2}}$

Possible Answers:

$\frac{1}{7^{x+6}}$

$7^{x+6}$

$7^{x+2}$

$-\frac{1}{7^{x+6}}$

$\frac{1}{7^{x+2}}$

Correct answer:

$7^{x+6}$

Explanation:

When dividing exponents, we subtract the exponents and keep the base the same.

$\frac{7^{8x+4}}{7^{7x-2}}=7^{8x+4-(7x-2)}=7^{8x+4-7x+2}=7^{x+6}$

Report an Error

Example Question #145 : Multiplying And Dividing Exponents

Simplify: $\frac{a+b}{a^2+2ab+b^2}$

Possible Answers:

a+b

$\frac{1}{a+ab+b}$

$\frac{1}{a+b}$

a-b

$\frac{1}{2ab}$

Correct answer:

$\frac{1}{a+b}$

Explanation:

Although it seems like we can't simplify anything, we do know that a^2+2ab+b^2=(a+b)^2 . Therefore we have:

$\frac{a+b}{a^2+2ab+b^2}=\frac{a+b}{(a+b)^2}$ . Now we can divide the exponents to get $(a+b)^{-1}=\frac{1}{a+b}$

Report an Error

Example Question #147 : Multiplying And Dividing Exponents

Simplify: $(\frac{x}{y})^{7n}*(\frac{x}{y^{-1}})^{2n}*\frac{y^{5n}}{x^{5n+2}}$

Possible Answers:

$x^{4n+2}$

$\frac{x^{4n}}{y^{2n}}$

$\frac{x^{4n-2}}{y^n}$

$\frac{x^n}{y^n}$

$x^{4n-2}$

Correct answer:

$x^{4n-2}$

Explanation:

Let's apply the exponential operation before we simplify.

$(\frac{x}{y})^{7n}*(\frac{x}{y^{-1}})^{2n}*\frac{y^{5n}}{x^{5n+2}}=\frac{x^{7n}}{y^{7n}}*x^{2n}y^{2n}*\frac{y^{5n}}{x^{5n+2}}$ In the numerator, the $y^{2n}, y^{5n}$ become $y^{7n}$ and cancels with the denominator in the left fraction.

We now have: $x^{7n}*x^{2n}*\frac{1}{x^{5n+2}}$ . By combining the top and applying the division rule of exponents, we get:

$x^{7n}*x^{2n}*\frac{1}{x^{5n+2}}=\frac{x^{9n}}{x^{5n+2}}=x^{9n-(5n+2)}=x^{9n-5n-2}=x^{4n-2}$

Report an Error

Example Question #146 : Multiplying And Dividing Exponents

Simplify: $\frac{2^{12}}{4^6}$

Possible Answers:

$\frac{1}{2}$

$-\frac{1}{4}$

$\frac{1}{4}$

Correct answer:

Explanation:

Although the exponents have different bases, we know that 4=2^2 . Therefore we can rewrite as $\frac{2^{12}}{4^6}=\frac{2^{12}}{(2^2)^6}=\frac{2^{12}}{2^{12}}=1$

Report an Error

Example Question #149 : Multiplying And Dividing Exponents

Simplify: $\frac{2^{24}8^8}{4^{16}}$

Possible Answers:

2^8

$2^{12}$

$\frac{1}{2^8}$

$2^{16}$

$\frac{1}{2^{12}}$

Correct answer:

$2^{16}$

Explanation:

Although the bases are not the same, we know that 8=2^3, 4=2^2 . We will base our answers in base of since this is present in all the choices. Therefore: $\frac{2^{24}8^8}{4^{16}}=\frac{2^{24}(2^3)^8}{(2^2)^{16}}=\frac{2^{24}2^{24}}{2^{32}}$ Now we add the exponents and then subtract them.

$\frac{2^{24}2^{24}}{2^{32}}=\frac{2^{48}}{2^{32}}=2^{16}$

Report an Error

View Algebra 2 Tutors

Andy
Certified Tutor

Villanova University, Bachelor of Science, Premedicine.

View Algebra 2 Tutors

Ping
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Computer Science. University of North Texas, Master of Arts, Education.

View Algebra 2 Tutors

Blake
Certified Tutor

Vanderbilt University, Bachelors, Neuroscience.

All Algebra II Resources

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

Popular Subjects

LSAT Tutors in New York City, MCAT Tutors in Dallas Fort Worth, Algebra Tutors in San Diego, ISEE Tutors in Washington DC, GMAT Tutors in Boston, Computer Science Tutors in Atlanta, Statistics Tutors in Denver, French Tutors in Los Angeles, Physics Tutors in Seattle, Algebra Tutors in Seattle

Popular Courses & Classes

ISEE Courses & Classes in Chicago, Spanish Courses & Classes in Boston, MCAT Courses & Classes in Washington DC, GMAT Courses & Classes in Houston, SSAT Courses & Classes in New York City, SSAT Courses & Classes in Miami, Spanish Courses & Classes in New York City, SSAT Courses & Classes in Los Angeles, ISEE Courses & Classes in Seattle, GRE Courses & Classes in Denver

Popular Test Prep

MCAT Test Prep in Houston, GMAT Test Prep in Los Angeles, GMAT Test Prep in Philadelphia, ISEE Test Prep in Houston, SSAT Test Prep in Miami, GMAT Test Prep in Houston, MCAT Test Prep in Atlanta, SAT Test Prep in Los Angeles, MCAT Test Prep in Seattle, SSAT 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 : Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #140 : Multiplying And Dividing Exponents

Example Question #141 : Multiplying And Dividing Exponents

Example Question #3602 : Algebra Ii

Example Question #142 : Multiplying And Dividing Exponents

Example Question #143 : Multiplying And Dividing Exponents

Example Question #144 : Multiplying And Dividing Exponents

Example Question #145 : Multiplying And Dividing Exponents

Example Question #147 : Multiplying And Dividing Exponents

Example Question #146 : Multiplying And Dividing Exponents

Example Question #149 : Multiplying And Dividing Exponents

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: