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

Example Question #51 : Negative Exponents

Evaluate $(-5)^{-4}$

Possible Answers:

$-\frac{1}{625}$

$\frac{1}{20}$

$\frac{1}{625}$

Correct answer:

$\frac{1}{625}$

Explanation:

When expressing negative exponents, we rewrite as such:

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

in which is the positive exponent raising base .

$(-5)^{-4}=\frac{1}{(-5)^4}=\frac{1}{625}$

Report an Error

Example Question #51 : Negative Exponents

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

Possible Answers:

$\frac{1}{8}$

$-\frac{1}{6}$

$-\frac{1}{8}$

Correct answer:

Explanation:

When expressing negative exponents, we rewrite as such:

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

in which is the positive exponent raising base .

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

Report an Error

Example Question #53 : Understanding Exponents

Evaluate $\frac{1}{6}^{-\frac{1}{2}}$

Possible Answers:

$\frac{\sqrt{6}}{6}$

$\sqrt{6}$

$-\sqrt{6}$

$\frac{1}{36}$

Correct answer:

$\sqrt{6}$

Explanation:

When dealing with fractional exponents, we rewrite as such:

$x^\frac{a}{b}=\sqrt[b]{x^a}$

in which is the index of the radical and is the exponent raising base .

When expressing negative exponents, we rewrite as such:

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

in which is the positive exponent raising base .

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

Report an Error

Example Question #51 : Exponents

Evaluate $12^{-\frac{1}{2}}$

Possible Answers:

$\frac{\sqrt{3}}{6}$

$\frac{1}{12}$

$2\sqrt{3}$

$6\sqrt{3}$

$\frac{\sqrt{3}}{2}$

Correct answer:

$\frac{\sqrt{3}}{6}$

Explanation:

When dealing with fractional exponents, we rewrite as such:

$x^\frac{a}{b}=\sqrt[b]{x^a}$

in which is the index of the radical and is the exponent raising base .

When expressing negative exponents, we rewrite as such:

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

in which is the positive exponent raising base .

$12^{-\frac{1}{2}}=\frac{1}{(\sqrt{12})}=\frac{1}{2{\sqrt{3}}}=\frac{\sqrt{3}}{6}$

Remember when getting rid of radicals, just multiply top and bottom by that radical.

Report an Error

Example Question #55 : Understanding Exponents

Evaluate $48^{-\frac{2}{3}}$

Possible Answers:

$\frac{\sqrt[3]{6}}{24}$

$\frac{\sqrt{3}}{24}$

$\frac{\sqrt{3}}{6}$

$\frac{\sqrt[3]{36}}{16}$

$\frac{\sqrt{6}}{16}$

Correct answer:

$\frac{\sqrt[3]{6}}{24}$

Explanation:

When dealing with fractional exponents, we rewrite as such:

$x^\frac{a}{b}=\sqrt[b]{x^a}$

in which is the index of the radical and is the exponent raising base .

When expressing negative exponents, we rewrite as such:

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

in which is the positive exponent raising base .

$48^{-\frac{2}{3}}=\frac{1}{\sqrt[3]{48^2}}=\frac{1}{\sqrt[3]{2304}}$

Let's find a perfect cube which is

64 =(4^3) .

$\frac{1}{\sqrt[3]{2304}}=\frac{1}{\sqrt[3]{64}*\sqrt[3]{36}}=\frac{1}{4\sqrt[3]{36}}$

To simplify, we need to multiply top and bottom by an appropriate cubic root. We know 36=6^2 so if we multiply top and bottom by $\sqrt[3]{6}$ we will get an integer in the denominator.

$\frac{1}{4\sqrt[3]{36}}*\frac{\sqrt[3]{6}}{\sqrt[3]{6}}=\frac{\sqrt[3]{6}}{4*6}=\frac{\sqrt[3]{6}}{24}$

Report an Error

Example Question #56 : Understanding Exponents

Evaluate $12^{-\frac{3}{4}}$

Possible Answers:

$\frac{\sqrt[4]{12}}{8}$

$\frac{\sqrt[4]{12}}{12}$

$\frac{\sqrt[3]{36}}{16}$

$\frac{\sqrt{6}}{12}$

$\frac{\sqrt[3]{12}}{12}$

Correct answer:

$\frac{\sqrt[4]{12}}{12}$

Explanation:

When dealing with fractional exponents, we rewrite as such:

$x^\frac{a}{b}=\sqrt[b]{x^a}$

in which is the index of the radical and is the exponent raising base .

When expressing negative exponents, we rewrite as such:

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

in which is the positive exponent raising base .

$12^{-\frac{3}{4}}=\frac{1}{\sqrt[4]{12^3}}=\frac{1}{\sqrt[4]{1728}}$

Let's find a perfect fourth power which is

16 = (2^4) .

$\frac{1}{\sqrt[4]{1728}}=\frac{1}{\sqrt[4]{16}*\sqrt[4]{108}}=\frac{1}{2\sqrt[4]{108}}$

To simplify, we need to multiply top and bottom by an appropriate fourth root. We know 108=3^3*2^2 .

We need to complete the numbers to the fourth power. It we multiply top and bottom by $\sqrt[4]{3*2^2}=\sqrt[4]{12}$ we will get an integer in the denominator.

$\frac{1}{2\sqrt[4]{108}}*\frac{\sqrt[4]{12}}{\sqrt[4]{12}}=\frac{\sqrt[4]{12}}{2*6}=\frac{\sqrt[4]{12}}{12}$

Report an Error

Example Question #51 : Exponents

Simplify $(4x^{2}y^{-6})(2x^{-7}y^{^3})$ .

Possible Answers:

$8x^{5}y^{3}$

$\frac{1}{8x^{14}y^{18}}$

$\frac{8}{x^{5}y^{3}}$

$\frac{1}{8x^{5}y^{3}}$

$\frac{8}{x^{14}y^{18}}$

Correct answer:

$\frac{8}{x^{5}y^{3}}$

Explanation:

First multiply the like terms, remembering that when multiplying terms that have exponents, you add the exponents.

$(4x^{2}y^{-6})(2x^{-7}y^{3})=(4\cdot 2)(x^{2}\cdot x^{-7})(y^{-6}\cdot y^{3})$

$=8x^{2-7}y^{-6+3}$

$=8x^{-5}y^{-3}$

Negative exponents indicate that the term should be in the denominator, so the final answer is:

$\frac{8}{x^{5}y^{3}}$

Report an Error

Example Question #58 : Understanding Exponents

Simplify: $6^{-2}+3^{-2}$

Possible Answers:

$\frac{5}{36}$

$\sqrt{6}+\sqrt{3}$

$\frac{1}{81}$

$\frac{5}{18}$

Correct answer:

$\frac{5}{36}$

Explanation:

Convert each negative exponent into fractional form.

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

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

Simplify the denominators.

$\frac{1}{36}+\frac{1}{9}$

Convert the second fraction with a common denominator of 36.

$\frac{1}{36}+\frac{4}{36}= \frac{5}{36}$

The answer is: $\frac{5}{36}$

Report an Error

Example Question #59 : Understanding Exponents

Evaluate: $2^{-3x}=8$

Possible Answers:

$-\frac{1}{4}$

$\textup{The answer is not given.}$

$-\frac{8}{3}$

$-\frac{2}{3}$

Correct answer:

Explanation:

In order to determine the value of x, we will need to convert the base of the right side similar to the left.

Eight is similar to two cubed. Rewrite the equation.

$2^{-3x}=2^3$

Now that our bases are the same, we can set the exponents equal to each other.

-3x=3

Divide by negative three on both sides.

$\frac{-3x}{-3}=\frac{3}{-3}$

The answer is: x=-1

Report an Error

Example Question #60 : Understanding Exponents

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

Possible Answers:

$\frac{1}{27x}$

27x

$\frac{x}{3}$

$\frac{1}{9x}$

Correct answer:

27x

Explanation:

The negative exponent can be converted into a fraction.

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

Rewrite the fraction.

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

Rewrite the complex fraction using a division sign.

$\frac{3x}{\frac{1}{3^{2}}} = 3x\div \frac{1}{3^2}$

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

$3x\times \frac{3^2}{1}=3x(9) = 27x$

The answer is: 27x

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

Biology Tutors in Chicago, Calculus Tutors in Phoenix, Math Tutors in Philadelphia, Biology Tutors in Atlanta, Reading Tutors in San Francisco-Bay Area, Calculus Tutors in Chicago, SSAT Tutors in Dallas Fort Worth, GRE Tutors in Phoenix, ACT Tutors in Dallas Fort Worth, Reading Tutors in Dallas Fort Worth

Popular Courses & Classes

Spanish Courses & Classes in Philadelphia, GMAT Courses & Classes in Washington DC, SSAT Courses & Classes in Houston, LSAT Courses & Classes in San Diego, SSAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Philadelphia, SSAT Courses & Classes in Los Angeles, LSAT Courses & Classes in New York City, SSAT Courses & Classes in Seattle, Spanish Courses & Classes in Washington DC

Popular Test Prep

LSAT Test Prep in San Diego, SSAT Test Prep in Miami, GMAT Test Prep in San Diego, GRE Test Prep in Houston, ISEE Test Prep in Phoenix, ACT Test Prep in Los Angeles, SSAT Test Prep in Philadelphia, ISEE Test Prep in San Diego, GMAT Test Prep in Washington DC, SAT 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 : Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #51 : Negative Exponents

Example Question #51 : Negative Exponents

Example Question #53 : Understanding Exponents

Example Question #51 : Exponents

Example Question #55 : Understanding Exponents

Example Question #56 : Understanding Exponents

Example Question #51 : Exponents

Example Question #58 : Understanding Exponents

Example Question #59 : Understanding Exponents

Example Question #60 : Understanding Exponents

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: