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

← Previous 1 2 … 5 6 7 8 9 10 11 12 13 … 30 31 Next →

Example Question #81 : Understanding Exponents

Solve the following: $8^{-2}-2^{-5}$

Possible Answers:

$-\frac{3}{64}$

$-\frac{1}{16}$

$-\frac{1}{64}$

$-\frac{1}{32}$

$-\frac{3}{32}$

Correct answer:

$-\frac{1}{64}$

Explanation:

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

The negative exponents can be rewritten into fractional form.

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

$8^{-2}-2^{-5} = \frac{1}{8^2}-\frac{1}{2^5} = \frac{1}{64}- \frac{1}{32}$

Convert the second fraction to match the denominator of the first fraction.

$\frac{1}{64}- \frac{1(2)}{32(2)} = \frac{1}{64}-\frac{2}{64}= -\frac{1}{64}$

The answer is: $-\frac{1}{64}$

Report an Error

Example Question #82 : Understanding Exponents

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

Possible Answers:

$\frac{1}{2}$

$\frac{27}{8}$

$\frac{9}{2}$

$\frac{27} {4}$

$\frac{9}{8}$

Correct answer:

$\frac{27}{8}$

Explanation:

Rewrite the negative exponent as the reciprocal of the positive power.

The negative exponent can be rewritten into a fraction as follows:

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

$(\frac{2}{3})^{-3}= \frac{1}{(\frac{2}{3})^3} = \frac{1}{\frac{8}{27}}$

Simplify the complex fraction.

$\frac{1}{\frac{8}{27}} = 1\div \frac{8}{27} = 1\times \frac{27}{8}= \frac{27}{8}$

The answer is: $\frac{27}{8}$

Report an Error

Example Question #83 : Understanding Exponents

Solve: $-4^{-3}-2^{-3}$

Possible Answers:

$-\frac{513}{64}$

$-\frac{513}{8}$

$\frac{11}{64}$

$-\frac{9}{513}$

$-\frac{9}{64}$

Correct answer:

$-\frac{9}{64}$

Explanation:

The negative exponents can be rewritten into a fraction.

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

Rewrite both terms given in the problem.

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

Find the least common denominator of both fractions.

$-\frac{1}{64}-\frac{1}{8} = -\frac{1}{64}-\frac{1(8)}{8(8)}$

Simplify the fractions.

$-\frac{1}{64}-\frac{8}{64}=-\frac{9}{64}$

The answer is: $-\frac{9}{64}$

Report an Error

Example Question #84 : Understanding Exponents

Solve: $-(-8^{-2})+8$

Possible Answers:

$7\frac{1}{8}$

$8\frac{1}{64}$

$8\frac{1}{16}$

$4\frac{1}{64}$

$7\frac{15}{16}$

Correct answer:

$8\frac{1}{64}$

Explanation:

Simplify the negative exponent as follows:

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

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

Rewrite the expression.

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

The answer is: $8\frac{1}{64}$

Report an Error

Example Question #85 : Understanding Exponents

Solve: $9^{-2}\times\frac{3}{ 2^{-4}}$

Possible Answers:

$\frac{3}{16}$

$\frac{1}{432}$

$\frac{16}{27}$

$\frac{1}{9}$

$\frac{8}{27}$

Correct answer:

$\frac{16}{27}$

Explanation:

Change all negative exponents into a fractional form by the following property.

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

$9^{-2}\times\frac{3}{ 2^{-4}} = \frac{1}{9^2} \times \frac{3}{\frac{1}{2^4}} = \frac{1}{81} \times \frac{3}{\frac{1}{16}}$

Simplify the fractions.

$\frac{1}{81} \times \frac{3}{\frac{1}{16}} = \frac{1}{81} \times 48 = \frac{48}{81}$

$\frac{48}{81} =\frac{16 \times 3}{27 \times 3}$

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

Report an Error

Example Question #81 : Exponents

Evaluate: $7^{-3}$

Possible Answers:

7^3

-7^3

$-\frac{1}{7^3}$

$\frac{1}{7^3}$

Correct answer:

$\frac{1}{7^3}$

Explanation:

When dealing with negative exponents, we write $x^{-a}=\frac{1}{x^a}$ . Therefore $7^{-3}=\frac{1}{7^3}$ .

Report an Error

Example Question #82 : Exponents

Evaluate: $(x+5)^{-3}$

Possible Answers:

$\frac{5^3}{(x+5)^3}$

$\frac{1}{x^3+5^3}$

$\frac{5^3}{x}$

$\frac{x}{5^3}$

$\frac{1}{(x+5)^3}$

Correct answer:

$\frac{1}{(x+5)^3}$

Explanation:

When dealing with negative exponents, we write $x^{-a}=\frac{1}{x^a}$ . Therefore $(x+5)^{-3}=\frac{1}{(x+5)^3}$

Report an Error

Example Question #83 : Exponents

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

Possible Answers:

$\frac{9}{4}$

$-\frac{4}{9}$

$\frac{4}{9}$

$-\frac{9}{4}$

Correct answer:

$\frac{9}{4}$

Explanation:

When dealing with negative exponents, we write $x^{-a}=\frac{1}{x^a}$ . Therefore $(\frac{2}{3})^{-2}=\frac{1}{(\frac{2}{3})^2}=\frac{1}{\frac{4}{9}}=\frac{9}{4}$ .

Report an Error

Example Question #84 : Exponents

Simplify: $(\frac{x}{6})^{-3}$

Possible Answers:

$-\frac{x^3}{256}$

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

$\frac{x^3}{256}$

$\frac{256}{x^3}$

$-\frac{256}{x^3}$

Correct answer:

$\frac{256}{x^3}$

Explanation:

When dealing with negative exponents, we write $x^{-a}=\frac{1}{x^a}$ . Therefore $(\frac{x}{6})^{-3}=\frac{1}{(\frac{x}{6})^3}=\frac{1}{\frac{x^3}{256}}=\frac{256}{x^3}$ .

Report an Error

Example Question #85 : Exponents

Evaluate: $3^{-4}$

Possible Answers:

$-\frac{1}{81}$

$\frac{1}{81}$

Correct answer:

$\frac{1}{81}$

Explanation:

When dealing with exponents, we convert as such: $x^{-a}=\frac{1}{x^a}$ . Therefore, $3^{-4}=\frac{1}{3^4}=\frac{1}{81}$ .

Report an Error

← Previous 1 2 … 5 6 7 8 9 10 11 12 13 … 30 31 Next →

View Algebra 2 Tutors

Jitendra
Certified Tutor

BHU, Bachelor, Mathematics.

View Algebra 2 Tutors

Thushan
Certified Tutor

Guilford Technical Community College, Associate in Science, Mechanical Engineering. North Carolina State University at Raleig...

View Algebra 2 Tutors

Mariam
Certified Tutor

Yarmouk University, Bachelor of Science, Mathematics. Touro College, Master of Science, Teacher Education, Multiple Levels.

All Algebra II Resources

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

Popular Subjects

French Tutors in Atlanta, Chemistry Tutors in Boston, Algebra Tutors in Philadelphia, Reading Tutors in San Francisco-Bay Area, SSAT Tutors in Washington DC, Statistics Tutors in Atlanta, Chemistry Tutors in Seattle, LSAT Tutors in Chicago, ISEE Tutors in Phoenix, Reading Tutors in Atlanta

Popular Courses & Classes

GRE Courses & Classes in Chicago, GRE Courses & Classes in Seattle, GRE Courses & Classes in Boston, ISEE Courses & Classes in Boston, ACT Courses & Classes in Miami, Spanish Courses & Classes in Atlanta, SSAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Miami, SAT Courses & Classes in Philadelphia, SAT Courses & Classes in Phoenix

Popular Test Prep

GRE Test Prep in Houston, LSAT Test Prep in Miami, SSAT Test Prep in Chicago, GRE Test Prep in Denver, GMAT Test Prep in Miami, GRE Test Prep in Chicago, ISEE Test Prep in Boston, ACT Test Prep in Miami, MCAT Test Prep in Houston, ACT Test Prep in Phoenix

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 #81 : Understanding Exponents

Example Question #82 : Understanding Exponents

Example Question #83 : Understanding Exponents

Example Question #84 : Understanding Exponents

Example Question #85 : Understanding Exponents

Example Question #81 : Exponents

Example Question #82 : Exponents

Example Question #83 : Exponents

Example Question #84 : Exponents

Example Question #85 : Exponents

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: