Call Now to Set Up Tutoring:

(888) 888-0446

College Algebra : Review and Other Topics

Study concepts, example questions & explanations for College Algebra

Create An Account

All College Algebra Resources

5 Diagnostic Tests 84 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #31 : Review And Other Topics

Evaluate.

$144^{1/2}$

Possible Answers:

$\pm22$

$\pm12$

$\pm36$

Correct answer:

$\pm12$

Explanation:

Exponents raised to a power of <1 can be written as the root of the denominator.

So:

$144^{1/2} = \sqrt[2]{144}=\pm12$

Recall that a square root can give two answers, one positive and one negative.

$\\(-12)(-12)=144 \\(12)(12)=144$

Report an Error

Example Question #3 : Rational Exponents

Evaluate

$8^{11/5}$

Possible Answers:

2.8

2.1

2.6

2.2

2.4

Correct answer:

2.2

Explanation:

$8^{11/5}$

The denominator of the exponent "N" is the same as the "N" root of that number.

$8^{11/5} = \sqrt[5]{8^{11}} = 2.2$

Report an Error

Example Question #3 : Rational Exponents

Evaluate

$(7^{5/3})^{3/4}$

Possible Answers:

11.478

14.215

10.582

13.569

11.386

Correct answer:

11.386

Explanation:

This appears more complicated than it is.

$(7^{5/3})^{3/4}$ is really just X^Y where

$X=7^{5/3}$

and

y=3/4

Re-written this equation looks like

$(\sqrt[3]{7^5})^{3/4} = 1.667^{3/4}= \sqrt[4]{1.667^3} = 11.386$

Report an Error

Example Question #1 : Rational Exponents

Evaluate

$17^{0.824}$

Possible Answers:

10.325

9.876

13.325

14.578

18.256

Correct answer:

10.325

Explanation:

$17^{0.824}$ can be seen as X^Y , in a scientific calculator use the X^Y button where Y=0.824 .

$17^{0.824}=10.325$

Report an Error

Example Question #4 : Rational Exponents

Evaluate the given rational exponent:

$8^{\frac{2}{3}}$

Possible Answers:

Correct answer:

Explanation:

Rational exponents can be simplified by following this common rule:

$a^{\frac{m}{n}}=\sqrt[n]{a^{m}}$

We can apply this concept to the given value in order to evaluate:

$\\8^{\frac{2}{3}}=\sqrt[3]{8^{2}}=\sqrt[3]{64}\\\sqrt[3]{64}=4$

Report an Error

Example Question #31 : Review And Other Topics

Solve for :

$81^{\frac{x}{4}}=27$

Possible Answers:

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

x=5

x=-1

x=3

x=1

Correct answer:

x=3

Explanation:

We can use the given property of rational exponents to solve for :

$a^\frac{m}{n}=\sqrt[n]{a^m}$

$\\81^{\frac{x}{4}}=\sqrt[4]{81^{x}}=27\\27^{4}=81^x\\81^{x}=531,441\\81^{3}=531,441\\x=3$

Report an Error

Example Question #12 : Rational Exponents

Solve for :

$32^{\frac{2}{x}}=4$

Possible Answers:

$x=\frac{4}{3}$

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

x=1

x=5

x=3

Correct answer:

x=5

Explanation:

We can use the given property of rational exponents to solve for :

$a^{\frac{m}{n}}=\sqrt[n]{a^m}$

$\\32^{\frac{2}{x}}=\sqrt[x]{32^2}=4\\\sqrt[x]{1024}=4\\4^{x}=1024\\4^{5}=1024\\x=5$

Report an Error

Example Question #13 : Rational Exponents

Evaluate: $(625)^{\frac {1}{4}}$

Possible Answers:

Correct answer:

Explanation:

Step 1: We need to understand what the fractional value in the exponent is.

A fractional exponent, $\frac {1}{n}$ , tells us that we must take the th root of the number.

In this case, we have $\frac {1}{4}$ , so we will take the 4th root of 625 .

Step 2: Calculate... $\sqrt_[4]{625}=5$

$\sqrt[4]{625}=\sqrt[4]{5*5*5*5}=5$

The answer is .

Report an Error

Example Question #31 : Review And Other Topics

Simplfy:

$\frac{x^{3.78}}{x^{2.58}}$

Possible Answers:

$x^{1.3}$

$x^{1.2}$

$x^{1.1}$

Correct answer:

$x^{1.2}$

Explanation:

Treat this with regular exponent rules.

$\frac{x^{3.78}}{x^{2.58}}=x^{3.78-2.58}=x^{1.2}$

Report an Error

Example Question #32 : Review And Other Topics

Simplify: $\frac{15x^2y^5c^3}{5xy^6c^3}$

Possible Answers:

$\frac{3x}{y}$

The answer is not present.

$\frac{3x}{yc}$

3xy

$\frac{3y}{x}$

Correct answer:

$\frac{3x}{y}$

Explanation:

$\frac{15x^2y^5c^3}{5xy^6c^3} \rightarrow 3xy^{-1}\rightarrow 3x*\frac{1}{y}=\boldsymbol{\frac{3x}{y}}$

Report an Error

View College Algebra Tutors

Charles
Certified Tutor

Pacific Intercontinental College, Master's/Graduate, Mathematics.

View College Algebra Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

View College Algebra Tutors

Jeremy
Certified Tutor

The University of Alabama, Bachelor in Arts, Religious Studies. University of West Alabama, Master of Arts, Social Sciences.

All College Algebra Resources

5 Diagnostic Tests 84 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

SSAT Tutors in San Francisco-Bay Area, Algebra Tutors in Houston, Spanish Tutors in Miami, LSAT Tutors in Washington DC, Math Tutors in Philadelphia, Biology Tutors in New York City, SSAT Tutors in Dallas Fort Worth, ISEE Tutors in Seattle, Computer Science Tutors in Los Angeles, Statistics Tutors in New York City

Popular Courses & Classes

SSAT Courses & Classes in Phoenix, GMAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Phoenix, GRE Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in New York City, SSAT Courses & Classes in Miami, Spanish Courses & Classes in Seattle, SSAT Courses & Classes in Philadelphia, GMAT Courses & Classes in Houston

Popular Test Prep

GRE Test Prep in Phoenix, SSAT Test Prep in Houston, GRE Test Prep in Boston, SSAT Test Prep in Boston, SSAT Test Prep in Phoenix, ACT Test Prep in Washington DC, ISEE Test Prep in Seattle, MCAT Test Prep in Phoenix, GMAT Test Prep in Atlanta, GRE Test Prep in Philadelphia

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

College Algebra : Review and Other Topics

Study concepts, example questions & explanations for College Algebra

All College Algebra Resources

Example Questions

Example Question #31 : Review And Other Topics

Example Question #3 : Rational Exponents

Example Question #3 : Rational Exponents

Example Question #1 : Rational Exponents

Example Question #4 : Rational Exponents

Example Question #31 : Review And Other Topics

Example Question #12 : Rational Exponents

Example Question #13 : Rational Exponents

Example Question #31 : Review And Other Topics

Example Question #32 : Review And Other Topics

All College Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: