We are open Saturday and Sunday!

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

← Previous 1 2 3 4 5 6 7 8 9 … 76 77 Next →

Example Question #41 : Understanding Exponents

Evaluate:

$24^{-2}$

Possible Answers:

$-\frac{1}{576}$

$\frac{1}{576}$

Correct answer:

$\frac{1}{576}$

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:

$24^{-2}=\frac{1}{24^2}=\frac{1}{576}$

Report an Error

Example Question #42 : Understanding Exponents

Evaluate:

$\left(\frac{1}{7}\right)^{-3}$

Possible Answers:

$\frac{1}{21}$

$-\frac{1}{343}$

343

$\frac{1}{343}$

Correct answer:

343

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:

$\left(\frac{1}{7}\right)^{-3}=\frac{1}{\frac{1}{7^3}}=\frac{1}{\frac{1}{343}}$

Dividing by a fraction is the same as multiplying by its reciprocal.

$\frac{1}{\frac{1}{343}}=1 \times \frac{343}{1}= 343$

Report an Error

Example Question #43 : Understanding Exponents

Evaluate:

$\left(\frac{2}{3}\right)^{-4}$

Possible Answers:

$\frac{81}{16}$

$-\frac{4}{9}$

$\frac{16}{81}$

$-\frac{81}{16}$

$-\frac{16}{81}$

Correct answer:

$\frac{81}{16}$

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:

$\left(\frac{2}{3}\right)^{-4}=\frac{1}{(\frac{2}{3})^3}=\frac{1}{\frac{16}{81}}$

Dividing by a fraction is the same as multiplying by its reciprocal.

$\frac{1}{\frac{16}{81}}=1\times\frac{81}{16}=\frac{81}{16}$

Report an Error

Example Question #44 : Understanding Exponents

Simplify: $12^{-12}$

Possible Answers:

$-12^{12}$

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

$12^{12}$

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

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

Correct answer:

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

Explanation:

When dealing with negative exponents, we convert to fractions as such: $x^{-a}=\frac{1}{x^a}$ which is the positive exponent raising base .

$12^{-12}=\frac{1}{12^{12}}$

Report an Error

Example Question #45 : Understanding Exponents

Simplify: $\frac{1}{64}^{-3}$

Possible Answers:

$\frac{1}{262144}$

$-\frac{1}{262144}$

262144

Correct answer:

262144

Explanation:

When dealing with negative exponents, we convert to fractions as such: $x^{-a}=\frac{1}{x^a}$ which is the positive exponent raising base .

$\frac{1}{64}^{-3}=\frac{1}{\frac{1}{64^3}}=\frac{1}{\frac{1}{262144}}=262144$

Report an Error

Example Question #46 : Understanding Exponents

Evaluate: $\frac{1}{64}^{-\frac{1}{3}}$

Possible Answers:

$\frac{1}{262144}$

$\frac{1}{4}$

Correct answer:

Explanation:

When dealing with fractional exponents, we rewrite as such: $x^{\frac{a}{b}}=\sqrt[b]{x^a}$ which is the index of the radical and is the exponent raising base . When dealing with negative exponents, we convert to fractions as such: $x^{-a}=\frac{1}{x^a}$ which is the positive exponent raising base .

$\frac{1}{64}^{-\frac{1}{3}}=\frac{1}{\frac{1}{\sqrt[3]{64}}}=\frac{1}{\frac{1}{4}}=4$

Report an Error

Example Question #47 : Understanding Exponents

Evaluate: $\frac{1}{8}^{-\frac{2}{3}}$

Possible Answers:

$-\frac{1}{12}$

$\frac{1}{2}$

$-\frac{1}{4}$

Correct answer:

Explanation:

$\frac{1}{8}^{-\frac{2}{3}}=\frac{1}{\frac{1}{\sqrt[3]{8^2}}}=\frac{1}{\frac{1}{4}}=4$

Report an Error

Example Question #48 : Understanding Exponents

Evaluate: $5^{-8}$

Possible Answers:

$-\frac{1}{5^8}$

$\frac{1}{5^{-8}}$

-5^8

$\frac{1}{5^8}$

$-5^{-8}$

Correct answer:

$\frac{1}{5^8}$

Explanation:

When dealing with negative exponents, we convert to fractions as such: $x^{-a}=\frac{1}{x^a}$ which is the positive exponent raising base .

$5^{-8}=\frac{1}{5^8}$

Report an Error

Example Question #49 : Understanding Exponents

Evaluate $21^{-2}$

Possible Answers:

$\frac{1}{441}$

$-\frac{1}{441}$

441

Correct answer:

$\frac{1}{441}$

Explanation:

When expressing negative exponents, we rewrite as such:

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

in which is the positive exponent raising base .

$21^{-2}=\frac{1}{21^2}=\frac{1}{441}$

Report an Error

Example Question #50 : Understanding Exponents

Evaluate $-4^{-4}$

Possible Answers:

$\frac{1}{16}$

$-\frac{1}{256}$

$-\frac{1}{16}$

$\frac{1}{256}$

Correct answer:

$-\frac{1}{256}$

Explanation:

When expressing negative exponents, we rewrite as such:

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

in which is the positive exponent raising base .

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

Report an Error

← Previous 1 2 3 4 5 6 7 8 9 … 76 77 Next →

View Algebra 2 Tutors

Eva
Certified Tutor

DePaul University, Bachelor in Arts, Neuroscience.

View Algebra 2 Tutors

Alexander
Certified Tutor

Cornell University, Bachelor of Science, Biological/Biosystems Engineering. Cleveland State University, Doctor of Philosophy,...

View Algebra 2 Tutors

Brittany
Certified Tutor

University of Cincinnati-Main Campus, Bachelor in Arts, Mathematics. Walden University, Master of Science, Education.

All Algebra II Resources

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

Popular Subjects

Algebra Tutors in San Francisco-Bay Area, Algebra Tutors in San Diego, LSAT Tutors in Miami, Spanish Tutors in Denver, ACT Tutors in Phoenix, Biology Tutors in New York City, SSAT Tutors in Phoenix, LSAT Tutors in Dallas Fort Worth, French Tutors in Miami, SAT Tutors in Boston

Popular Courses & Classes

SAT Courses & Classes in Washington DC, GMAT Courses & Classes in Washington DC, SSAT Courses & Classes in Washington DC, SAT Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Chicago, GMAT Courses & Classes in Atlanta, SSAT Courses & Classes in Seattle, SAT Courses & Classes in New York City, GRE Courses & Classes in Washington DC, ACT Courses & Classes in San Diego

Popular Test Prep

GRE Test Prep in Chicago, ACT Test Prep in San Diego, GMAT Test Prep in Philadelphia, ISEE Test Prep in Washington DC, MCAT Test Prep in Seattle, SAT Test Prep in Phoenix, GMAT Test Prep in Washington DC, GMAT Test Prep in Atlanta, GMAT Test Prep in Houston, ISEE 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 : Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #41 : Understanding Exponents

Example Question #42 : Understanding Exponents

Example Question #43 : Understanding Exponents

Example Question #44 : Understanding Exponents

Example Question #45 : Understanding Exponents

Example Question #46 : Understanding Exponents

Example Question #47 : Understanding Exponents

Example Question #48 : Understanding Exponents

Example Question #49 : Understanding Exponents

Example Question #50 : Understanding Exponents

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: