Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Algebra II

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 #3281 : Algebra Ii

Evaluate $256^{-\frac{1}{2}}$ .

Possible Answers:

128

$-\frac{1}{16}$

$\frac{1}{16}$

Correct answer:

$\frac{1}{16}$

Explanation:

When an exponent is negative, we rewrite in this form in terms of fraction:

$a^{-b}=\frac{1}{a^b}$

is the base while is the exponent and it's going to be a postive number when written in a fraction.

$x^{\frac{a}{b}}=\sqrt[b]{x^a}$

is the exponent from the numerator of the fraction, is the index from the denominator of the fraction and is the base of the exponent.

$256^{-\frac{1}{2}}=(\frac{1}{256})^{\frac{1}{2}}=\sqrt{\frac{1}{256}}=\frac{1}{16}$

Report an Error

Example Question #3281 : Algebra Ii

Simplify:

$48^{\frac{1}{2}}$

Possible Answers:

$4\sqrt{3}$

$2\sqrt{6}$

$2\sqrt{3}$

Correct answer:

$4\sqrt{3}$

Explanation:

When we have fractional exponents, we convert like this:

$x^{\frac{a}b{}}=\sqrt[b]{x^a}$ . is the index of the radical which is the denominator of the fractional exponent, is the power that will raise the base which is the numerator of the fractional exponent and is the base.

$48^{\frac{1}{2}}=\sqrt{48}=\sqrt{16*3}=4\sqrt{3}$

Report an Error

Example Question #31 : Fractional Exponents

Simplify:

$\frac{1}{8}^{\frac{1}{3}}$

Possible Answers:

$\frac{1}{4}$

$\frac{1}{2}$

$\frac{1}{16}$

$\frac{1}{24}$

$\frac{1}{8}$

Correct answer:

$\frac{1}{2}$

Explanation:

When we have fractional exponents, we convert like this:

$\frac{1}{8}^{\frac{1}{3}}=\sqrt[3]{\frac{1}{8}}=\frac{1}{2}$

Report an Error

Example Question #3283 : Algebra Ii

Evaluate:

$9^{\frac{1}{2}}$

Possible Answers:

4.5

$\frac{1}{9}$

$\pm3$

$\frac{1}{81}$

Correct answer:

$\pm3$

Explanation:

When exponents are in fraction, there are turned into this form:

$x^{\frac{a}{b}}=\sqrt[b]{x^a}$ where represents the index of the radical which is the denominator of the fractional exponent, is the power raising base . is the numerator of the fractional exponent.

$9^{\frac{1}{2}}=\sqrt{9}=\pm3$

Report an Error

Example Question #3285 : Algebra Ii

Evaluate:

$\frac{49}{64}^{\frac{1}{2}}$

Possible Answers:

$\pm\frac{7}{8}$

$\frac{11}{12}$

$\frac{3}{4}$

$\frac{2401}{4096}$

$\frac{98}{125}$

Correct answer:

$\pm\frac{7}{8}$

Explanation:

When exponents are in fraction, there are turned into this form:

$x^{\frac{a}{b}}=\sqrt[b]{x^a}$

where represents the index of the radical which is the denominator of the fractional exponent, is the power raising base . is the numerator of the fractional exponent.

$\frac{49}{64}^{\frac{1}{2}}=\sqrt{\frac{49}{64}}=\pm\frac{7}{8}$

Report an Error

Example Question #32 : Fractional Exponents

Evaluate:

$16^{\frac{1}{2}}$

Possible Answers:

$\frac{1}{4}$

$\frac{1}{2}$

$\frac{1}{8}$

Correct answer:

Explanation:

When exponents are fractional, we express them using the following format:

$x^{\frac{a}{b}}=\sqrt[b]{x^a}$

In this format, is the index of the radical found in the denominator of the fractional exponent and is the exponent found in the numerator of the fractional exponent by raising the base of .

$16^{\frac{1}{2}}=\sqrt{16}=4$

Report an Error

Example Question #3282 : Algebra Ii

Evaluate:

$216^{\frac{2}{3}}$

Possible Answers:

Correct answer:

Explanation:

When exponents are fractional, we express them using the following format:

$x^{\frac{a}{b}}=\sqrt[b]{x^a}$

In this format, is the index of the radical found in the denominator of the fractional exponent and is the exponent found in the numerator of the fractional exponent by raising the base of .

$216^{\frac{2}{3}}=\sqrt[3]{216^2}=\sqrt[3]{(6^3)^2}=6^2=36$

Report an Error

Example Question #3286 : Algebra Ii

Evaluate:

$512^{\frac{1}{3}}$

Possible Answers:

Correct answer:

Explanation:

In order to evaluate fractional exponents, we can express them using the following relationship:

$x^{\frac{a}{b}}=\sqrt[b]{x^a}$

In this formula, represents the index of the radical from the denominator of the fraction and is the exponent that raises the base: .

We can then rewrite and solve the expression in the following way.

$512^{\frac{1}{3}}=\sqrt[3]{512^1}=8$

Report an Error

Example Question #3287 : Algebra Ii

Evaluate:

$256^{\frac{1}{4}}$

Possible Answers:

Correct answer:

Explanation:

In order to evaluate fractional exponents, we can express them using the following relationship:

$x^{\frac{a}{b}}=\sqrt[b]{x^a}$

In this formula, represents the index of the radical from the denominator of the fraction and is the exponent that raises the base: .

We can then rewrite and solve the expression in the following way.

$256^{\frac{1}{4}}=\sqrt[4]{256}=4$

Report an Error

Example Question #3288 : Algebra Ii

Evaluate:

$729^{-\frac{1}{3}}$

Possible Answers:

$-\frac{1}{9}$

$\frac{1}{9}$

$\frac{1}{3}$

$-\frac{1}{3}$

Correct answer:

$\frac{1}{9}$

Explanation:

In order to evaluate fractional exponents, we can express them using the following relationship:

$x^{\frac{a}{b}}=\sqrt[b]{x^a}$

In this formula, represents the index of the radical from the denominator of the fraction and is the exponent that raises the base: . When exponents are negative, we can express them using the following relationship:

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

We can then rewrite and solve the expression in the following way.

$729^{-\frac{1}{3}}=\frac{1}{\sqrt[3]{729}}=\frac{1}{9}$

Report an Error

View Algebra 2 Tutors

Laura
Certified Tutor

New York University, Bachelor in Arts, French.

View Algebra 2 Tutors

Emmanuel
Certified Tutor

Baylor University, Bachelor of Science, Biology, General.

View Algebra 2 Tutors

Shakeel
Certified Tutor

All Algebra II Resources

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

Popular Subjects

GRE Tutors in Philadelphia, GMAT Tutors in Chicago, Reading Tutors in Philadelphia, French Tutors in Dallas Fort Worth, ISEE Tutors in Dallas Fort Worth, MCAT Tutors in Boston, ACT Tutors in Washington DC, ISEE Tutors in Boston, GRE Tutors in Chicago, MCAT Tutors in New York City

Popular Courses & Classes

ACT Courses & Classes in Philadelphia, LSAT Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Houston, GRE Courses & Classes in Miami, SAT Courses & Classes in New York City, SSAT Courses & Classes in Miami, GRE Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Houston, GMAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Phoenix

Popular Test Prep

LSAT Test Prep in Los Angeles, LSAT Test Prep in Philadelphia, ACT Test Prep in Los Angeles, GMAT Test Prep in Washington DC, SSAT Test Prep in Atlanta, MCAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Philadelphia, GRE Test Prep in Washington DC, SSAT Test Prep in Dallas Fort Worth, SAT Test Prep in Chicago

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 : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #3281 : Algebra Ii

Example Question #3281 : Algebra Ii

Example Question #31 : Fractional Exponents

Example Question #3283 : Algebra Ii

Example Question #3285 : Algebra Ii

Example Question #32 : Fractional Exponents

Example Question #3282 : Algebra Ii

Example Question #3286 : Algebra Ii

Example Question #3287 : Algebra Ii

Example Question #3288 : Algebra Ii

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: