We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

College Algebra : Real Exponents

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 #1 : Real Exponents

Simplfy:

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

Possible Answers:

$x^{1.1}$

$x^{1.3}$

$x^{1.2}$

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 #2 : Real Exponents

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

Possible Answers:

$\frac{3x}{y}$

$\frac{3x}{yc}$

The answer is not present.

$\frac{3y}{x}$

3xy

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

Example Question #3 : Real Exponents

Simplify the following expression.

$(2x^{7.2})(x^{-6.2})$

Possible Answers:

2x^2

$x^{1.2}$

$2x^{13.2}$

Correct answer:

Explanation:

When multiplying exponential, the exponents always add. While the 2 in the front of the first exponential might throw you off, you may disregard it initially.

$(2)(x^{7.2}x^{-6.2})$

Which simplifies to

$(2)x^{7.2-6.2}=(2)x^1$

Our final answer is

Report an Error

Example Question #4 : Real Exponents

Simplify the following expression:

$\frac{(x^{2})^{5}x^{-8}}{x^2}$

Possible Answers:

x^3

x^2

Correct answer:

Explanation:

First, we need to simplify the numerator. First term, (x^2)^5 can be simplified to $x^{10}$ . Plugging this back into the numerator, we get

$x^{10}x^{-8}$ , which simplifies to x^2 . Plugging this back into the original equation gives us

$\frac{x^2}{x^2}$ , which is simply .

Report an Error

Example Question #3 : Real Exponents

Solve for :

$a^{2}\cdot a^{3}= 243$

Possible Answers:

a=2

a=5

a=4

a=3

a=6

Correct answer:

a=3

Explanation:

When like bases with exponents are multiplied, the value of the product's exponent is the sum of both original exponents as shown here:

$a^{n}\cdot a^{m}=a^{n+m}$

We can use this common rule to solve for in the practice problem:

$\\a^{2}\cdot a^{3}=243\\a^{2}\cdot a^{3}=a^{2+3}\\a^{5}=243$

$a=\sqrt[5]{243}\\a=3$

Report an Error

Example Question #3 : Real Exponents

Solve for :

$\frac{a^{7}}{a^3}=256$

Possible Answers:

a=5

a=7

a=3

a=6

a=4

Correct answer:

a=4

Explanation:

The product of dividing like bases with exponents is the difference of the numerator and denominator exponents. This is a common rule when working with rational exponents:

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

We can use this common rule to solve for :

$\\\frac{a^{7}}{a^{3}}=256\\\\a^{7-3}=256\\a^{4}=256\\a=\sqrt[4]{256}\\a=4$

Report an Error

Example Question #4 : Real Exponents

Solve for :

$3^{x-2}\cdot9^{2x}=27$

Possible Answers:

x=0

x=1

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

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

x=-1

Correct answer:

x=1

Explanation:

To solve for , we need all values to have like bases:

$\\3^{x-2}\cdot9^{2x}=27\\3^{x-2}\cdot3^{2\cdot2x}=27\\3^{x-2}\cdot3^{4x}=3^{3}$

Now that all values have like bases, we can solve for :

$\\x-2+4x=3\\5x-2=3\\5x=5\\x=1$

Report an Error

Example Question #6 : Real Exponents

Solve for :

$27^{\frac{x-3}{3}}\cdot3^{\frac{3x}{4}}=81$

Possible Answers:

x=3

x=-4

x=4

x=0

x=-3

Correct answer:

x=4

Explanation:

To solve for , we want all values in the equation to have like bases:

$\\27^{\frac{x-3}{3}}\cdot3^{\frac{3x}{4}}=81 \\3^{3\cdot\frac{x-3}{3}}\cdot3^{\frac{3x}{4}}=3^{4} \\3^{x-3}\cdot3^{\frac{3x}{4}}=3^{4}$

Now we can solve for :

$\\x-3+\frac{3x}{4}=4\\\frac{7x}{4}=7\\7x=28\\x=4$

Report an Error

Example Question #5 : Real Exponents

Solve for :

$5^{\frac{x}{4}}\cdot5^{\frac{x}{8}}=125$

Possible Answers:

x=4

x=16

x=12

x=24

x=8

Correct answer:

x=8

Explanation:

To solve for , we want all the values in the equation to have like bases:

$\\5^{\frac{x}{4}}\cdot5^{\frac{x}{8}}=125 \\5^{\frac{x}{4}}\cdot5^{\frac{x}{8}}=5^3$

Now we can solve for :

$\\\frac{x}{4}+\frac{x}{8}=3 \\8\cdot(\frac{x}{4}+\frac{x}{8})=3\cdot8 \\2x+x=24\\3x=24\\x=8$

Report an Error

Example Question #6 : Real Exponents

Simplify the following expression.

$\frac{x^{\sqrt{2}}}{x^2}*\frac{x^{\sqrt{2}}}{x^2}$

Possible Answers:

x^2

$x^{-2}$

$x^{\sqrt{2}}$

Correct answer:

$x^{-2}$

Explanation:

The original expression can be rewritten as

$(\frac{x^{\sqrt{2}}}{x^2})^2$ . Whenever you can a fraction raised to a power, that power gets distributed out to the numerator and denominator. In mathematical terms, the new expression is

$\frac{x^{2}}{x^4}$ , which simply becomes $\frac{1}{x^2}$ , or $x^{-2}$

Report an Error

View College Algebra Tutors

Zara
Certified Tutor

University of Manitoba, Bachelor in Arts, Mathematics.

View College Algebra Tutors

George
Certified Tutor

Pensacola State College, Bachelor in Arts, Mathematics.

View College Algebra Tutors

Shakeel
Certified Tutor

All College Algebra Resources

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

Popular Subjects

ISEE Tutors in Seattle, SSAT Tutors in Los Angeles, SAT Tutors in Phoenix, Reading Tutors in Chicago, MCAT Tutors in San Francisco-Bay Area, Math Tutors in Denver, Math Tutors in Atlanta, ISEE Tutors in Philadelphia, SSAT Tutors in Phoenix, GMAT Tutors in New York City

Popular Courses & Classes

LSAT Courses & Classes in Boston, GMAT Courses & Classes in San Diego, ISEE Courses & Classes in Seattle, SSAT Courses & Classes in Seattle, GRE Courses & Classes in New York City, ACT Courses & Classes in San Diego, MCAT Courses & Classes in Denver, ISEE Courses & Classes in San Diego, MCAT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Boston

Popular Test Prep

MCAT Test Prep in Houston, SSAT Test Prep in Washington DC, LSAT Test Prep in Washington DC, GMAT Test Prep in San Diego, MCAT Test Prep in Phoenix, SAT Test Prep in Miami, SAT Test Prep in Phoenix, SSAT Test Prep in Phoenix, ISEE Test Prep in Philadelphia, 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 : Real Exponents

Study concepts, example questions & explanations for College Algebra

All College Algebra Resources

Example Questions

Example Question #1 : Real Exponents

Example Question #2 : Real Exponents

Example Question #3 : Real Exponents

Example Question #4 : Real Exponents

Example Question #3 : Real Exponents

Example Question #3 : Real Exponents

Example Question #4 : Real Exponents

Example Question #6 : Real Exponents

Example Question #5 : Real Exponents

Example Question #6 : Real Exponents

All College Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: