We are open Saturday and Sunday!

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

← Previous 1 2 3 4 5 6 7 8 9 … 13 14 Next →

Example Question #21 : Integer Exponents

Solve: $2(5^{-3})$

Possible Answers:

$\frac{1}{1000}$

$\frac{2}{125}$

$-\frac{1}{30}$

$-\frac{2}{125}$

Correct answer:

$\frac{2}{125}$

Explanation:

Evaluate the negative exponential first.

$5^{-3} =\frac{1}{5^3} = \frac{1}{125}$

Replace the fraction.

$2(5^{-3}) =2 (\frac{1}{125})= \frac{2}{125}$

The answer is: $\frac{2}{125}$

Report an Error

Example Question #21 : Review And Other Topics

What is the value of $(\frac{2}{3})^4$ ?

Possible Answers:

$\frac{16}{81}$

$\frac{8}{81}$

$\frac{4}{3}$

$\frac{4}{15}$

Correct answer:

$\frac{16}{81}$

Explanation:

A value raised to the fourth power will multiply itself four times.

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

The answer is: $\frac{16}{81}$

Report an Error

Example Question #21 : Integer Exponents

Evaluate: 2^6+3^4-5^3

Possible Answers:

Correct answer:

Explanation:

Step 1: Evaluate each term separately...

2^6=2*2*2*2*2*2=64

3^4=3*3*3*3=81

5^3=5*5*5=125

Step 2: Re-write statement using the converted numbers.

64+81-125

Add:

145-125

Simplify:

Report an Error

Example Question #22 : Review And Other Topics

Express $5^{-3}$ with only positive exponents.

Possible Answers:

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

$\frac {1}{625}$

No Solution

$\frac {1}{5^2}$

Correct answer:

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

Explanation:

Whenever we have a negative exponent in a exponential term, we change the term..

We write divided by the term to make the exponent positive..

So.. $5^{-3}=\frac {1}{5^3}$

Report an Error

Example Question #301 : College Algebra

Evaluate: 2^2-3^2+16

Possible Answers:

Correct answer:

Explanation:

Step 1: Expand each term:

2^2=2*2, 3^2=3*3, 16=16

Step 2: Multiply to find the value of each term..

2^2=4,3^2=9, 16

Step 3: Re-write the original question, replacing the exponents with the numbers we calculated...

4-9+16

Step 4: Add/Subtract

4-9=-5

-5+16=11

Report an Error

Example Question #10 : Fractional Exponents

Simplify: $25^{\frac{3}{2}}$

Possible Answers:

125

Correct answer:

125

Explanation:

An option to solve this is to split up the fraction. Rewrite the fractional exponent as follows:

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

A value to its half power is the square root of that value.

$25^{\frac{1}{2}} = \sqrt{25}=5$

Substitute this value back into $(25^{\frac{1}{2}})^3$ .

$(25^{\frac{1}{2}})^3 = (5)^3 = 5\times 5\times 5 = 125$

Report an Error

Example Question #1 : Rational Exponents

Which of the following is equivalent to $b^{\frac{4}{5}}$ ?

Possible Answers:

$\sqrt[4]{b^5}$

$\sqrt[5]{b^4}$

$\sqrt[4]{b^{-5}}$

5b^4

Correct answer:

$\sqrt[5]{b^4}$

Explanation:

Which of the following is equivalent to $b^{\frac{4}{5}}$ ?

When dealing with fractional exponents, keep the following in mind: The numerator is making the base bigger, so treat it like a regular exponent. The denominator is making the base smaller, so it must be the root you are taking.

This means that $b^{\frac{4}{5}}$ is equal to the fifth root of b to the fourth. Perhaps a bit confusing, but it means that we will keep b^4 , but put the whole thing under $\sqrt[5]{b}$ .

So if we put it together we get:

$\sqrt[5]{b^4}$

Report an Error

Example Question #11 : Fractional Exponents

Evaluate $\frac{1}{4}^{-\frac{1}{2}}$

Possible Answers:

$-\frac{1}{16}$

$\frac{1}{4}$

$\frac{1}{16}$

Correct answer:

Explanation:

When dealing with fractional exponents, remember this form:

$\sqrt[a]{x^n}$ is the index of the radical which is also the denominator of the fraction, represents the base of the exponent, and is the power the base is raised to. That value is the numerator of the fraction.

With a negative exponent, we need to remember this form:

$\frac{1}{x^n}$ represents the base of the exponent, and is the power in a positive value.

$\frac{1}{4}^{-\frac{1}{2}}=\frac{1}{\frac{1}{4}^{\frac{1}{2}}}=\frac{1}{\sqrt[2]{\frac{1}{4^1}}}=\frac{1}{\frac{1}{2}}=2$

Report an Error

Example Question #3 : Rational Exponents

$\left ( \frac{125}{343} \right )^{\frac{2}{3}}$

Possible Answers:

$\frac{5}{7}$

$\frac{25}{49}$

$\frac{5}{343}$

$\frac{625}{2401}$

$\frac{250}{686}$

Correct answer:

$\frac{25}{49}$

Explanation:

First, distribute the exponent to both the numerator and denominator of the fraction.

$\frac{125^{\frac{2}{3}}}{343^{\frac{2}{3}}}$

The numerator of a fractional exponent is the power you take the number to and the denominator is the root that you take the number to.

$\frac{\sqrt[3]{125^{2}}}{\sqrt[3]{343^{2}}}$

You can take the cubed root and square the numbers in either order but if you can do the root first that is often easier.

$\frac{5^{2}}{7^{2}}$

$\frac{25}{49}$

This is the answer. Alternatively, you could have squared the numbers first before taking the cubed root.

$\frac{\sqrt[3]{15625}}{\sqrt[3]{117649}}$

$\frac{25}{49}$

Report an Error

Example Question #4 : Rational Exponents

Evaluate:

$\left(\frac{1}{256}\right)^{-\frac{1}{4}}$

Possible Answers:

$-\frac{1}{4}$

Correct answer:

Explanation:

In order to evaluate fractional exponents, we can express them using the following relationship:

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

In this formula, represents the index of the radical from the denominator of the fraction and is the exponent that raises the base: . When exponents are negative, we can express them using the following relationship:

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

We can then rewrite and solve the expression in the following way.

$\left(\frac{1}{256}\right)^{-\frac{1}{4}}=\frac{1}{\frac{1}{\sqrt[4]{256}}}=\frac{1}{\frac{1}{4}}$

Dividing by a fraction is the same as multiplying by its reciprocal.

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

Report an Error

← Previous 1 2 3 4 5 6 7 8 9 … 13 14 Next →

View College Algebra Tutors

Odysseas
Certified Tutor

University of New Hampshire at Manchester, Master of Science, Civil Engineering. National Technical University of Athens, Doc...

View College Algebra Tutors

Kayley
Certified Tutor

New Mexico State University-Main Campus, Bachelor of Science, Biology, General.

View College Algebra Tutors

Akunna
Certified Tutor

Bergen Community College, Associate in Science, Natural Sciences. Long Island University-Brooklyn Campus, Current Grad Studen...

All College Algebra Resources

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

Popular Subjects

Spanish Tutors in Miami, Physics Tutors in San Francisco-Bay Area, Algebra Tutors in Miami, MCAT Tutors in Seattle, French Tutors in San Francisco-Bay Area, MCAT Tutors in Houston, SAT Tutors in Denver, Computer Science Tutors in Dallas Fort Worth, ACT Tutors in San Francisco-Bay Area, ISEE Tutors in Miami

Popular Courses & Classes

Spanish Courses & Classes in Chicago, LSAT Courses & Classes in San Diego, ISEE Courses & Classes in Boston, GRE Courses & Classes in Boston, ACT Courses & Classes in Phoenix, GMAT Courses & Classes in Washington DC, Spanish Courses & Classes in Los Angeles, ISEE Courses & Classes in Miami, SAT Courses & Classes in Miami, GRE Courses & Classes in Dallas Fort Worth

Popular Test Prep

GRE Test Prep in Atlanta, GRE Test Prep in New York City, ACT Test Prep in Houston, ACT Test Prep in Phoenix, GRE Test Prep in Washington DC, SAT Test Prep in Los Angeles, SAT Test Prep in New York City, MCAT Test Prep in Houston, GRE Test Prep in Boston, GMAT Test Prep in Washington DC

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 #21 : Integer Exponents

Example Question #21 : Review And Other Topics

Example Question #21 : Integer Exponents

Example Question #22 : Review And Other Topics

Example Question #301 : College Algebra

Example Question #10 : Fractional Exponents

Example Question #1 : Rational Exponents

Example Question #11 : Fractional Exponents

Example Question #3 : Rational Exponents

Example Question #4 : Rational Exponents

All College Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: