Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Mathematical Relationships and Basic Graphs

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:

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

$x^{15}$

$-\frac{1}{x}$

$\frac{1}{x}$

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:

$x^{-4}y^7$

x^4y^7

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

(xy)^4

(xy)^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:

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

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

5^4

-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:

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

$7^{x+2}$

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

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

$7^{x+6}$

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 #146 : Multiplying And Dividing Exponents

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

Possible Answers:

a-b

$\frac{1}{2ab}$

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

a+b

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

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 #145 : Multiplying And Dividing Exponents

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

Possible Answers:

$-\frac{1}{4}$

$\frac{1}{4}$

$\frac{1}{2}$

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

Abe
Certified Tutor

CUNY Brooklyn College, Bachelor of Science, Accounting and Business Management. CUNY Graduate School and University Center, M...

View Algebra 2 Tutors

Jack
Certified Tutor

University of Washington-Seattle Campus, Bachelor in Arts, Mathematics. Western Washington University, Master of Science, Mat...

View Algebra 2 Tutors

Om
Certified Tutor

Pune University India, Bachelor of Science, Physics. CUNY Graduate School and University Center, Doctor of Philosophy, Nuclea...

All Algebra II Resources

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

Popular Subjects

English Tutors in Dallas Fort Worth, SAT Tutors in Washington DC, ISEE Tutors in Boston, LSAT Tutors in Chicago, GRE Tutors in Washington DC, LSAT Tutors in New York City, French Tutors in San Diego, Chemistry Tutors in Miami, French Tutors in Miami, Calculus Tutors in Dallas Fort Worth

Popular Courses & Classes

MCAT Courses & Classes in New York City, GRE Courses & Classes in Denver, GMAT Courses & Classes in Miami, SAT Courses & Classes in Los Angeles, LSAT Courses & Classes in Houston, ACT Courses & Classes in Los Angeles, ACT Courses & Classes in Houston, Spanish Courses & Classes in Chicago, ISEE Courses & Classes in Los Angeles, GMAT Courses & Classes in Boston

Popular Test Prep

SSAT Test Prep in Phoenix, GRE Test Prep in Philadelphia, SAT Test Prep in Houston, SAT Test Prep in New York City, GRE Test Prep in Denver, SAT Test Prep in Chicago, MCAT Test Prep in Los Angeles, SSAT Test Prep in Miami, ACT Test Prep in Seattle, GRE 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 : Mathematical Relationships and Basic Graphs

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 #146 : Multiplying And Dividing Exponents

Example Question #147 : Multiplying And Dividing Exponents

Example Question #145 : 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: