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 #61 : Understanding Exponents

Evaluate: $(\frac{4}{5})^{-2}$

Possible Answers:

$\frac{25}{16}$

$\frac{25}{8}$

$\frac{2\sqrt5}{5}$

$\frac{16}{25}$

$\frac{8}{25}$

Correct answer:

$\frac{25}{16}$

Explanation:

Rewrite the negative exponent as a fraction.

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

Following this rule, rewrite the given expression.

$(\frac{4}{5})^{-2}=\frac{1}{(\frac{4}{5})^2} = \frac{1}{\frac{4}{5} \cdot \frac{4}{5}}= \frac{1}{\frac{16}{25}}$

Take the reciprocal of the denominator to eliminate the complex fraction.

The answer is: $\frac{25}{16}$

Report an Error

Example Question #61 : Understanding Exponents

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

Possible Answers:

$\sqrt2 +\sqrt3$

$\frac{5}{18}$

$\frac{2}{27}$

$\frac{11}{18}$

$\frac{1}{36}$

Correct answer:

$\frac{11}{18}$

Explanation:

To eliminate the negative exponent, we will need to convert the terms to a fraction.

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

According to this rule, convert both terms.

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

Simplify the fractions.

$\frac{1}{2}+\frac{1}{9} = \frac{9}{18}+ \frac{2}{18} =\frac{11}{18}$

The answer is: $\frac{11}{18}$

Report an Error

Example Question #63 : Understanding Exponents

Simplify: $\frac{6^{-3}}{8^{-3}}$

Possible Answers:

$\frac{3}{4}$

$\frac{4}{3}$

$\frac{4096}{729}$

$\frac{27}{64}$

$\frac{64}{27}$

Correct answer:

$\frac{64}{27}$

Explanation:

Convert the numerator and denominator to fractions by using the formula below.

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

$\frac{6^{-3}}{8^{-3}} = \frac{\frac{1}{6^3}}{\frac{1}{8^3}}$

Rewrite the fractions using a division sign.

$\frac{\frac{1}{6^3}}{\frac{1}{8^3}} =\frac{1}{6^3} \div\frac{1}{8^3}$

Take the reciprocal of the second term and change the division sign to a multiplication symbol.

$\frac{1}{6^3} \times 8^3 = \frac{8^3}{6^3} = \frac{8\cdot 8\cdot 8}{6\cdot 6\cdot 6} =\frac{4\cdot 4\cdot 4}{3\cdot 3\cdot 3} = \frac{64}{27}$

The answer is: $\frac{64}{27}$

Report an Error

Example Question #61 : Negative Exponents

Evaluate the exponents: $\frac{2^{-1}+3^{-1}}{2^{-2}-3^{-2}}$

Possible Answers:

Correct answer:

Explanation:

Write the rule for negative exponents.

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

Convert the powers on the numerator and denominator.

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

Add the numerator. Find the least common denominator and add the numerators.

$\frac{1}{2}+\frac{1}{3} = \frac{3}{6}+\frac{2}{6} = \frac{5}{6}$

Subtract the denominator also by converting to the least common denominator.

$\frac{1}{4}-\frac{1}{9} = \frac{9}{36}-\frac{4}{36} = \frac{5}{36}$

Divide the numerator with the denominator. Convert the complex fraction by rewriting it using a division sign. Swap the numerator and denominator of the second term and change the division sign to a multiplication sign.

$\frac{\frac{5}{6}}{\frac{5}{36}} = \frac{5}{6}\div \frac{5}{36} = \frac{5}{6}\times \frac{36}{5} = 6$

The answer is:

Report an Error

Example Question #61 : Exponents

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

Possible Answers:

$\frac{3}{256}$

$\frac{1}{2304}$

2304

$\frac{256}{9}$

$\frac{256}{3}$

Correct answer:

$\frac{1}{2304}$

Explanation:

Whenever we have a negative exponent, we can convert that to a fraction.

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

Evaluate the inner term.

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

The complex fraction can be reduced as follows:

$\frac{3}{\frac{1}{16}} = 3\div \frac{1}{16} = 3\times \frac{16}{1} = 48$

Substitute this value into the parentheses.

$(48)^{-2} = \frac{1}{48^2} = \frac{1}{2304}$

The answer is: $\frac{1}{2304}$

Report an Error

Example Question #66 : Understanding Exponents

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

Possible Answers:

$\frac{4}{49}$

$\frac{7}{4}$

$\frac{49}{4}$

$\frac{49}{2}$

$\frac{2}{49}$

Correct answer:

$\frac{49}{4}$

Explanation:

Convert the negative exponent as follows:

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

Rewrite the expression without the negative exponent.

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

Rewrite the complex fraction using a division sign.

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

The answer is: $\frac{49}{4}$

Report an Error

Example Question #67 : Understanding Exponents

Simplify $7^{-6}$

Possible Answers:

$-\frac{1}{7^6}$

$-\frac{1}{42}$

$\frac{1}{7^6}$

$\frac{6}{7}$

$\frac{1}{42}$

Correct answer:

$\frac{1}{7^6}$

Explanation:

We evaluate negative exponents as

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

which is the positive exponent raising base .

Therefore

$7^{-6}=\frac{1}{7^6}$ .

Report an Error

Example Question #68 : Understanding Exponents

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

Possible Answers:

$\frac{1}{27}$

$-\frac{1}{27}$

Correct answer:

Explanation:

We evaluate negative exponents as

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

which is the positive exponent raising base .

Therefore

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

Report an Error

Example Question #69 : Understanding Exponents

Determine the value of: $4^{-2}-2^{-6}$

Possible Answers:

$\frac{1}{12}$

$\frac{1}{32}$

$\frac{1}{16}$

$\frac{3}{32}$

$\frac{3}{64}$

Correct answer:

$\frac{3}{64}$

Explanation:

The negative exponents can be rewritten as a fraction.

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

Convert the terms.

$4^{-2}-2^{-6} = \frac{1}{4^2}-\frac{1}{2^6} = \frac{1}{16}- \frac{1}{64}$

Convert the first fraction so that the denominator are similar.

$\frac{1}{16}- \frac{1}{64} = \frac{1(4)}{16(4)}- \frac{1}{64} = \frac{4}{64}-\frac{1}{64}$

Subtract the numerators.

The answer is: $\frac{3}{64}$

Report an Error

Example Question #70 : Understanding Exponents

Simplify: $(\frac{3}{5})^{-2}$

Possible Answers:

$\frac{3}{25}$

$\frac{9}{25}$

$\frac{3\sqrt5}{5}$

$\frac{1}{3}$

$\frac{25}{9}$

Correct answer:

$\frac{25}{9}$

Explanation:

To eliminate the negative exponent, use the following property:

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

Rewrite the expression using this property.

$(\frac{3}{5})^{-2} = \frac{1}{(\frac{3}{5})^2} = \frac{1}{(\frac{3}{5})(\frac{3}{5})} = \frac{1}{\frac{9}{25}}$

Simplify the complex fraction.

$\frac{1}{\frac{9}{25}} =1\div \frac{9}{25} =1\times \frac{25} {9} =\frac{25}{9}$

The answer is: $\frac{25}{9}$

Report an Error

View Algebra 2 Tutors

Michelle
Certified Tutor

University of Nevada-Las Vegas, Bachelor of Science, Mathematics.

View Algebra 2 Tutors

Dejuan
Certified Tutor

University of Illinois at Urbana-Champaign, Bachelor of Science, Electrical Engineering.

View Algebra 2 Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

All Algebra II Resources

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

Popular Subjects

GRE Tutors in Miami, Calculus Tutors in Seattle, Algebra Tutors in Houston, Computer Science Tutors in San Diego, Reading Tutors in Seattle, LSAT Tutors in Washington DC, Computer Science Tutors in Washington DC, Spanish Tutors in New York City, SAT Tutors in Atlanta, GRE Tutors in Chicago

Popular Courses & Classes

SSAT Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Seattle, SSAT Courses & Classes in Los Angeles, ACT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in San Diego, LSAT Courses & Classes in Los Angeles, ISEE Courses & Classes in Houston, GRE Courses & Classes in New York City, Spanish Courses & Classes in Seattle, GMAT Courses & Classes in Chicago

Popular Test Prep

MCAT Test Prep in Philadelphia, SSAT Test Prep in Miami, SAT Test Prep in San Diego, GRE Test Prep in San Diego, GMAT Test Prep in San Francisco-Bay Area, GRE Test Prep in Denver, SAT Test Prep in Denver, SAT Test Prep in Washington DC, ACT Test Prep in Chicago, SSAT 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 : Understanding Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #61 : Understanding Exponents

Example Question #61 : Understanding Exponents

Example Question #63 : Understanding Exponents

Example Question #61 : Negative Exponents

Example Question #61 : Exponents

Example Question #66 : Understanding Exponents

Example Question #67 : Understanding Exponents

Example Question #68 : Understanding Exponents

Example Question #69 : Understanding Exponents

Example Question #70 : Understanding Exponents

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: