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 #3233 : Algebra Ii

Evaluate: $7^{-1}-2(3)^{-1}$

Possible Answers:

$-\frac{1}{42}$

$-\frac{17}{21}$

$-\frac{3}{7}$

$-\frac{1}{21}$

$-\frac{11}{21}$

Correct answer:

$-\frac{11}{21}$

Explanation:

In order to evaluate this, we will first need to rewrite the negative exponents fractions.

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

Rewrite each term.

$7^{-1}-2(3)^{-1} = \frac{1}{7} - 2(\frac{1}{3}) = \frac{1}{7}-\frac{2}{3}$

Determine the least common denominator by multiplying both denominators together.

$\frac{1}{7}-\frac{2}{3} = \frac{1(3)}{7(3)}-\frac{2(7)}{3(7)} = \frac{3}{21}-\frac{14}{21}$

Subtract the numerator.

The answer is: $-\frac{11}{21}$

Report an Error

Example Question #3234 : Algebra Ii

Simplify: $2(3^{-2})-3(2^{-2})+6^{-1}$

Possible Answers:

$\frac{41}{36}$

$-\frac{13}{3}$

$-\frac{13}{36}$

$-\frac{27}{12}$

$\frac{7}{6}$

Correct answer:

$-\frac{13}{36}$

Explanation:

Rewrite all negative exponential into fractions.

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

$2(3^{-2})-3(2^{-2})+6^{-1} = 2(\frac{1}{3^2})-3(\frac{1}{2^2})+\frac{1}{6}$

Simplify the terms.

$\frac{2}{9}-\frac{3}{4}+\frac{1}{6}$

Determine the least common factor by writing out the multiples of each denominator.

9-[9,18,27,36]

4-[4,8,12,16,20,24,28,32,36]

6-[6,12,18,24,30,36]

Convert each fraction to a common denominator of 36.

$\frac{2}{9}-\frac{3}{4}+\frac{1}{6}=\frac{2(4)}{9(4)}-\frac{3(9)}{4(9)}+\frac{1(6)}{6(6)}$

Simplify the fractions.

$\frac{8}{36}-\frac{27}{36}+\frac{6}{36} = -\frac{13}{36}$

The answer is: $-\frac{13}{36}$

Report an Error

Example Question #101 : Understanding Exponents

Simplify: $\frac{(3^{-2})^{-1}}{2^{-1}}$

Possible Answers:

$\frac{2}{9}$

$\frac{1}{9}$

$\frac{1}{18}$

$\frac{1}{36}$

Correct answer:

Explanation:

Simplify the numerator by product of exponents.

$\frac{(3^{-2})^{-1}}{2^{-1}}=\frac{3^2}{2^{-1}}= \frac{9}{2^{-1}}$

Rewrite the negative exponent as a fraction.

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

$\frac{9}{2^{-1}} = \frac{9}{\frac{1}{2}}= 9\div \frac{1}{2}$

Convert the division sign to a multiplication sign and take the reciprocal of the second term.

$9\times \frac{2}{1} =18$

The answer is:

Report an Error

Example Question #3231 : Algebra Ii

Solve: $(\frac{1}{3})^{-3}$

Possible Answers:

$\frac{1}{27}$

$\frac{1}{9}$

$-\frac{1}{9}$

Correct answer:

Explanation:

In order to evaluate this expression, we will need to rewrite the negative exponent as a fraction.

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

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

Simplify the denominator.

$\frac{1}{\frac{1}{27}} = 1\div \frac{1}{27} = 1\times \frac{27}{1} = 27$

The answer is:

Report an Error

Example Question #3232 : Algebra Ii

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

Possible Answers:

$\frac{9}{8}$

$\frac{27}{16}$

$\frac{16}{27}$

$\frac{1}{432}$

$\frac{8}{27}$

Correct answer:

$\frac{27}{16}$

Explanation:

In order to simplify this expression, we will need to reconvert the negative exponents to fractions.

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

Rewrite the fraction.

$\frac{2^{-4}}{3^{-3}} = \frac{\frac{1}{2^4}}{\frac{1}{3^3}} = \frac{\frac{1}{16}}{\frac{1}{27}}$

Rewrite the complex fraction using a division sign.

$\frac{\frac{1}{16}}{\frac{1}{27}} = \frac{1}{16}\div \frac{1}{27} = \frac{1}{16}\times \frac{27} {1}$

The answer is: $\frac{27}{16}$

Report an Error

Example Question #3238 : Algebra Ii

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

Possible Answers:

$\frac{1}{128}$

128

$\frac{1}{2}$

$\frac{1}{64}$

Correct answer:

$\frac{1}{128}$

Explanation:

We will need to convert both negative exponents into fractions.

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

The expression becomes:

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

Evaluate each term.

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

$\frac{1}{(\frac{1}{2})^{3}} = \frac{1}{\frac{1}{8}} = 1\div \frac{1}{8} = 1\times \frac{8}{1}=8$

This means that:

$\frac{\frac{1}{4^{2}}}{\frac{1}{(\frac{1}{2})^{3}}} = \frac{1}{16} \div 8 = \frac{1}{16}\times \frac{1}{8}$

The answer is: $\frac{1}{128}$

Report an Error

Example Question #3239 : Algebra Ii

Solve: $3(\frac{5}{3})^{-3}$

Possible Answers:

$\frac{125}{9}$

$\frac{125}{81}$

$\frac{9}{125}$

$\frac{81}{125}$

$\frac{1}{125}$

Correct answer:

$\frac{81}{125}$

Explanation:

Rewrite the negative exponential term as a fraction.

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

Rewrite the expression.

$3(\frac{5}{3})^{-3} = 3\cdot \frac{1}{(\frac{5}{3})^3} = 3\cdot \frac{1}{(\frac{125}{27})}$

Simplify the second term.

$\frac{1}{(\frac{125}{27})} = 1\div \frac{125}{27} = 1\times \frac{27} {125}=\frac{27} {125}$

Replace the term.

$3\cdot \frac{1}{(\frac{125}{27})} = 3\cdot \frac{27}{125}$

Multiply the whole number with the numerator.

The answer is: $\frac{81}{125}$

Report an Error

Example Question #101 : Exponents

Solve: $2(\frac{2}{7})^ {-2}$

Possible Answers:

$\frac{8}{7}$

$\frac{8}{49}$

$\frac{49}{2}$

$\frac{343}{4}$

$\frac{7}{2}$

Correct answer:

$\frac{49}{2}$

Explanation:

Solve by first rewriting the term with the negative exponent as a fraction.

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

Simplify the complex fraction.

$\frac{1}{\frac{4}{49}} = 1\div \frac{4}{49} =1 \times \frac{49}{4}=\frac{49}{4}$

The expression becomes:

$2\cdot \frac{1}{\frac{4}{49}} = 2\cdot \frac{49}{4} = \frac{49}{2}$

The answer is: $\frac{49}{2}$

Report an Error

Example Question #3241 : Algebra Ii

Evaluate: $(\frac{3^{-2}}{6^{-1}})^{-2}$

Possible Answers:

$\frac{9}{4}$

2916

$\frac{1}{2916}$

$\frac{9}{16}$

$\frac{16}{9}$

Correct answer:

$\frac{9}{4}$

Explanation:

To evaluate a negative exponent, it is the reciprocal of the positive power.

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

Evaluate each term.

$3^{-2} = \frac{1}{3^2} =\frac{1}{9}$

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

Divide both fractions.

$(\frac{3^{-2}}{6^{-1}}) = \frac{1}{9}\div \frac{1}{6} = \frac{1}{9}\times \frac{6}{1} = \frac{2}{3}$

The original expression was: $(\frac{3^{-2}}{6^{-1}})^{-2}$

Replace the term and repeat the process for solving negative exponents.

$(\frac{3^{-2}}{6^{-1}})^{-2} = (\frac{2}{3})^{-2} = \frac{1}{(\frac{2}{3})^2} = \frac{1}{\frac{4}{9}}$

The answer is: $\frac{9}{4}$

Report an Error

Example Question #101 : Exponents

Solve: $3^{-1}+3^{-2}-3^{-3}$

Possible Answers:

$\frac{13}{27}$

$\frac{11}{27}$

$\frac{7}{27}$

$-\frac{11}{27}$

$\frac{4}{27}$

Correct answer:

$\frac{11}{27}$

Explanation:

Convert all terms with negative exponents to fractional form.

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

$3^{-1}+3^{-2}-3^{-3} =\frac{1}{3^{1}}+\frac{1}{3^2}-\frac{1}{3^3}$

$\frac{1}{3}+\frac{1}{9}-\frac{1}{27}$

Convert all fractions to a common denominator. Visually, the LCD can be seen as 27, since this value is divisible by all three terms.

$\frac{1(9)}{3(9)}+\frac{1(3)}{9(3)}-\frac{1}{27} = \frac{9}{27}+ \frac{3}{27}- \frac{1}{27}$

The answer is: $\frac{11}{27}$

Report an Error

View Algebra 2 Tutors

Thien
Certified Tutor

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

View Algebra 2 Tutors

Steven
Certified Tutor

University of Louisville, Bachelor of Science, Mechanical Engineering. University of Phoenix-Louisville Campus, Master of Eng...

View Algebra 2 Tutors

James
Certified Tutor

University of Georgia, Bachelor in Arts, Political Science and Government.

All Algebra II Resources

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

Popular Subjects

MCAT Tutors in Houston, Biology Tutors in Denver, Computer Science Tutors in Boston, Calculus Tutors in Philadelphia, Math Tutors in San Francisco-Bay Area, LSAT Tutors in Dallas Fort Worth, SSAT Tutors in Atlanta, Biology Tutors in Chicago, English Tutors in Houston, MCAT Tutors in Seattle

Popular Courses & Classes

ACT Courses & Classes in Houston, SSAT Courses & Classes in Seattle, GRE Courses & Classes in Seattle, ISEE Courses & Classes in Boston, LSAT Courses & Classes in Boston, SAT Courses & Classes in Seattle, GRE Courses & Classes in Los Angeles, GMAT Courses & Classes in Atlanta, SAT Courses & Classes in Los Angeles, SSAT Courses & Classes in Chicago

Popular Test Prep

ACT Test Prep in Houston, LSAT Test Prep in Dallas Fort Worth, LSAT Test Prep in San Diego, MCAT Test Prep in New York City, SAT Test Prep in Atlanta, SSAT Test Prep in Washington DC, ACT Test Prep in Denver, GRE Test Prep in Boston, GMAT Test Prep in Denver, GRE 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 : Understanding Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #3233 : Algebra Ii

Example Question #3234 : Algebra Ii

Example Question #101 : Understanding Exponents

Example Question #3231 : Algebra Ii

Example Question #3232 : Algebra Ii

Example Question #3238 : Algebra Ii

Example Question #3239 : Algebra Ii

Example Question #101 : Exponents

Example Question #3241 : Algebra Ii

Example Question #101 : Exponents

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: