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 #501 : Mathematical Relationships And Basic Graphs

Express $-3^{-3}$ as a fraction.

Possible Answers:

$-\frac{1}{9}$

$-\frac{1}{27}$

$\frac{1}{27}$

Correct answer:

$-\frac{1}{27}$

Explanation:

When an exponent is negative, we rewrite in this form in terms of a 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.

$-3^{-3}=\frac{1}{(-3)^3}=-\frac{1}{27}$

Report an Error

Example Question #31 : Negative Exponents

Evaluate $5^{-0.5}$ .

Possible Answers:

$\sqrt{5}}{}$

$-\frac{1}{5}$

$\frac{\sqrt{5}}{5}$

$-\frac{\sqrt{5}}{5}$

$\frac{1}{5}$

Correct answer:

$\frac{\sqrt{5}}{5}$

Explanation:

When an exponent is negative, we rewrite in this form in terms of a 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.

When an exponent is a decimal, we convert to a fraction.

$0.5=\frac{1}{2}$

This is then written in radical form.

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

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.

$5^{-0.5}=\frac{1}{(5)^{0.5}}=\frac{1}{\sqrt{5}}=\frac{\sqrt{5}}{5}$

Report an Error

Example Question #31 : Exponents

Simplify $\frac{1}{4}^{-\frac{1}{2}}$ .

Possible Answers:

$\frac{1}{16}$

$-\frac{1}{4}$

$-\frac{1}{2}$

Correct answer:

Explanation:

When an exponent is negative, we rewrite in this form in terms of a 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.

When an exponent is a fraction, we convert to radical form.

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

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.

$\frac{1}{4}^{-\frac{1}{2}}=(\frac{1}{\frac{1}{4}})^{\frac{1}{2}}=\sqrt{\frac{1}{\frac{1}{4}}}=2$

Report an Error

Example Question #31 : Exponents

Simplify:

$10^{-5}$

Possible Answers:

-10^5

$-\frac{1}{10^5}$

$\frac{1}{10^5}$

1000

10000

Correct answer:

$\frac{1}{10^5}$

Explanation:

When an exponent is negative, we express as such:

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

is the positive exponent, and is the base.

$10^{-5}=\frac{1}{10^5}= \frac{1}{100000}$ .

Report an Error

Example Question #501 : Mathematical Relationships And Basic Graphs

Simplify:

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

Possible Answers:

$\frac{1}{2}$

$\frac{1}{4}$

$-\frac{1}{4}$

Correct answer:

Explanation:

When an exponent is negative, we express as such:

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

is the positive exponent, and is the base.

$\frac{1}{2}^{-2}=\frac{1}{\frac{1}{2^2}}=\frac{1}{\frac{1}{4}}=4$

Report an Error

Example Question #31 : Negative Exponents

Simplify:

$(-2)^{-2}$

Possible Answers:

$\frac{1}{4}$

$-\frac{1}{4}$

Correct answer:

$\frac{1}{4}$

Explanation:

When an exponent is negative, we express as such:

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

is the positive exponent, and is the base.

$(-2)^{-2}=\frac{1}{(-2)^2}=\frac{1}{4}$

Report an Error

Example Question #501 : Mathematical Relationships And Basic Graphs

Simplify:

$-3^{-3}$

Possible Answers:

$-\frac{1}{9}$

$-\frac{1}{27}$

$\frac{1}{27}$

$\frac{1}{9}$

Correct answer:

$-\frac{1}{27}$

Explanation:

When an exponent is negative, we express as such:

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

is the positive exponent, and is the base.

$-3^{-3}=-\frac{1}{3^3}=-\frac{1}{27}$

Remember the negative sign is not part of the base value.

Report an Error

Example Question #501 : Mathematical Relationships And Basic Graphs

Evaluate:

$15^{-4}$

Possible Answers:

$-\frac{1}{15^4}$

$\frac{1}{15^4}$

$15^{4}$

-15^4

Correct answer:

$\frac{1}{15^4}$

Explanation:

In order to convert negative exponents, we will use the following formula:

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

In this formula, is the positive exponent and is the base.

$15^{-4}=\frac{1}{15^4}$

Report an Error

Example Question #39 : Understanding Exponents

Evaluate:

$(\frac{1}{6})^{-3}$

Possible Answers:

216

$-\frac{1}{6^3}$

$\frac{1}{6^3}$

Correct answer:

216

Explanation:

In order to convert negative exponents, we will use the following formula:

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

In this formula, is the positive exponent and is the base.

$6^{-3}=\frac{1}{(\frac{1}{6})^3}=\frac{1}{\frac{1}{216}}=216$

Report an Error

Example Question #31 : Negative Exponents

Evaluate:

$18^{-1}$

Possible Answers:

$\frac{1}{18}$

$-\frac{1}{18}$

Correct answer:

$\frac{1}{18}$

Explanation:

When exponents are negative, we can express them using the following relationship:

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

In this format, represents the base and represents the exponent. A negative exponent becomes positive when it is rewritten as a reciprocal.

Therefore:

$18^{-1}=\frac{1}{18^1}=\frac{1}{18}$

Report an Error

View Algebra 2 Tutors

Thien
Certified Tutor

University of Mary Washington, Bachelor of Science, Biology, General.

View Algebra 2 Tutors

Jose
Certified Tutor

State University of New York at Albany, Bachelor of Science, Applied Mathematics. Teachers College at Columbia University, Ma...

View Algebra 2 Tutors

Manuel O.
Certified Tutor

Pedagogical Institute - Cuba, Bachelor of Science, Physics.

All Algebra II Resources

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

Popular Subjects

GRE Tutors in Boston, Physics Tutors in New York City, Reading Tutors in Miami, Physics Tutors in Chicago, English Tutors in Phoenix, LSAT Tutors in Miami, GMAT Tutors in Miami, LSAT Tutors in New York City, Biology Tutors in Miami, English Tutors in Boston

Popular Courses & Classes

SSAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Atlanta, GMAT Courses & Classes in Philadelphia, SAT Courses & Classes in Denver, Spanish Courses & Classes in Houston, Spanish Courses & Classes in Boston, ACT Courses & Classes in Philadelphia, MCAT Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Phoenix, SSAT Courses & Classes in Houston

Popular Test Prep

GMAT Test Prep in Philadelphia, SAT Test Prep in Atlanta, SSAT Test Prep in Chicago, LSAT Test Prep in Washington DC, SAT Test Prep in Miami, SSAT Test Prep in Denver, SSAT Test Prep in Washington DC, ACT Test Prep in Philadelphia, LSAT Test Prep in Boston, GMAT 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 : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #501 : Mathematical Relationships And Basic Graphs

Example Question #31 : Negative Exponents

Example Question #31 : Exponents

Example Question #31 : Exponents

Example Question #501 : Mathematical Relationships And Basic Graphs

Example Question #31 : Negative Exponents

Example Question #501 : Mathematical Relationships And Basic Graphs

Example Question #501 : Mathematical Relationships And Basic Graphs

Example Question #39 : Understanding Exponents

Example Question #31 : Negative Exponents

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: