We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Understanding 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 #91 : Exponents

Evaluate: $4^{-4}$

Possible Answers:

$\frac{1}{256}$

$\frac{1}{16}$

$-\frac{1}{16}$

$-\frac{1}{256}$

Correct answer:

$\frac{1}{256}$

Explanation:

When dealing with exponents, we convert as such: $x^{-a}=\frac{1}{x^a}$ . Therefore $4^{-4}=\frac{1}{4^4}=\frac{1}{256}$

Report an Error

Example Question #92 : Exponents

Simplify: $x^{-3}$

Possible Answers:

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

-3x

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

x^3

-x^3

Correct answer:

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

Explanation:

When dealing with exponents, we convert as such: $x^{-a}=\frac{1}{x^a}$ . Therefore, $x^{-3}=\frac{1}{x^3}$ .

Report an Error

Example Question #93 : Exponents

Evaluate: $-x^{-4}$

Possible Answers:

x^4

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

$\frac{1}{(-x)^4}$

-x^4

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

Correct answer:

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

Explanation:

When dealing with exponents, we convert as such: $x^{-a}=\frac{1}{x^a}$ . Therefore, $-x^4=-\frac{1}{x^4}$ . Remember since there's a negative sign outside the exponent, we apply the negative sign afterwards.

Report an Error

Example Question #94 : Exponents

Simplify: $(\frac{4}{x})^{-5}$

Possible Answers:

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

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

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

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

-4^5x^5

Correct answer:

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

Explanation:

When dealing with exponents, we convert as such: $x^{-a}=\frac{1}{x^a}$ . Therefore, $(\frac{4}{x})^{-5}=\frac{1}{\frac{4}{x}^{5}}=\frac{1}{\frac{4^5}{x^5}}=\frac{x^5}{4^5}$

Report an Error

Example Question #95 : Exponents

Simplify: $(-2x)^{-4}$

Possible Answers:

16x^4

-16x^4

$\frac{1}{16x^4}$

$\frac{1}{12x^4}$

$-\frac{1}{16x^4}$

Correct answer:

$\frac{1}{16x^4}$

Explanation:

When dealing with exponents, we convert as such: $x^{-a}=\frac{1}{x^a}$ . Therefore, $(-2x)^{-4}=\frac{1}{(-2x)^4}=\frac{1}{16x^4}$ . Remember when applying exponents to the base, we need to apply the exponent to also the coefficient in front of the variable.

Report an Error

Example Question #96 : Negative Exponents

Simplify: $\frac{7}{49^{-2}}$

Possible Answers:

$\frac{1}{49}$

$\frac{1}{343}$

$\frac{1}{2401}$

16807

2401

Correct answer:

16807

Explanation:

Convert the negative exponent to a fraction.

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

$\frac{7}{49^{-2}} = \frac{7}{\frac{1}{49^{2}}} = 7\times 49^2 = 7\times 2401$

Simplify this term.

The answer is: 16807

Report an Error

Example Question #97 : Negative Exponents

Evaluate: $(\frac{4}{7})^{-2}+4^{-1}$

Possible Answers:

$\frac{212}{49}$

$\frac{97}{18}$

$\frac{113}{196}$

$\frac{33}{17}$

$\frac{53}{16}$

Correct answer:

$\frac{53}{16}$

Explanation:

Rewrite the expression as fractions. The negative exponent will need to be eliminated in order to be simplified.

$(\frac{4}{7})^{-2} = \frac{1}{(\frac{4}{7})^2} = \frac{1}{\frac{16}{49}} =\frac{49}{16}$

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

Add the expression.

$(\frac{4}{7})^{-2}+4^{-1}= \frac{49}{16}+ \frac{1}{4}$

Convert the second fraction so that both fractions have common denominators.

$\frac{49}{16}+ \frac{4}{16} = \frac{53}{16}$

The answer is: $\frac{53}{16}$

Report an Error

Example Question #98 : Negative Exponents

Evaluate: $\frac{2(4^{-3})}{8^{-2}}$

Possible Answers:

$\frac{1}{4}$

$\frac{1}{2}$

$\frac{2}{3}$

Correct answer:

Explanation:

Rewrite the negative exponents as fractions.

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

$8^{-2} = \frac{1}{8^2} = \frac{1}{64}$

Replace the terms.

$\frac{2(4^{-3})}{8^{-2}}=\frac{2 (\frac{1}{64})}{(\frac{1}{64})} =2$

The answer is:

Report an Error

Example Question #91 : Negative Exponents

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

Possible Answers:

$\frac{9}{4}$

$\frac{9}{7}$

$\frac{16}{81}$

$\frac{9}{4}$

$\frac{81}{16}$

Correct answer:

$\frac{81}{16}$

Explanation:

We will need to convert the negative exponent into a fraction. This is equivalent to the reciprocal of the positive power.

$(\frac{2}{3})^{-4} = \frac{1}{(\frac{2}{3})^{4}}$

Simplify the complex fraction.

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

The answer is: $\frac{81}{16}$

Report an Error

Example Question #3232 : Algebra Ii

Evaluate: $5^{-2} \times 2(2^{-1})$

Possible Answers:

$\frac{1}{100}$

$\frac{1}{25}$

$\frac{26}{25}$

$\frac{1}{50}$

$\frac{6}{25}$

Correct answer:

$\frac{1}{25}$

Explanation:

The negative exponents can be rewritten as fractions.

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

Change the expression.

$5^{-2} \times 2(2^{-1}) = \frac{1}{25}\times 2(\frac{1}{2}) = \frac{1}{25}$

The answer is: $\frac{1}{25}$

Report an Error

View Algebra 2 Tutors

MEER
Certified Tutor

IIT , Master's/Graduate, Microelectronics .

View Algebra 2 Tutors

Margaret
Certified Tutor

View Algebra 2 Tutors

Lucciana
Certified Tutor

Miami Dade College, Bachelor of Science, Biology, General.

All Algebra II Resources

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

Popular Subjects

Computer Science Tutors in Houston, SSAT Tutors in San Diego, Spanish Tutors in Los Angeles, Biology Tutors in San Francisco-Bay Area, French Tutors in Seattle, LSAT Tutors in Boston, MCAT Tutors in Seattle, GMAT Tutors in San Francisco-Bay Area, English Tutors in Atlanta, LSAT Tutors in Denver

Popular Courses & Classes

SAT Courses & Classes in Philadelphia, LSAT Courses & Classes in Philadelphia, GMAT Courses & Classes in Los Angeles, SSAT Courses & Classes in Boston, ACT Courses & Classes in Atlanta, ACT Courses & Classes in San Diego, Spanish Courses & Classes in Chicago, MCAT Courses & Classes in Denver, GRE Courses & Classes in San Diego, SSAT Courses & Classes in Chicago

Popular Test Prep

ACT Test Prep in New York City, ACT Test Prep in Washington DC, ISEE Test Prep in Los Angeles, GRE Test Prep in San Diego, ACT Test Prep in Los Angeles, GRE Test Prep in Seattle, SSAT Test Prep in San Francisco-Bay Area, GRE Test Prep in Dallas Fort Worth, ACT Test Prep in Seattle, SAT 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 : Understanding Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #91 : Exponents

Example Question #92 : Exponents

Example Question #93 : Exponents

Example Question #94 : Exponents

Example Question #95 : Exponents

Example Question #96 : Negative Exponents

Example Question #97 : Negative Exponents

Example Question #98 : Negative Exponents

Example Question #91 : Negative Exponents

Example Question #3232 : Algebra Ii

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: