Call Now to Set Up Tutoring:

(888) 888-0446

PSAT Math : How to find a rational number from an exponent

Study concepts, example questions & explanations for PSAT Math

Create An Account

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1201 : Psat Mathematics

$Simplify: \frac{\sqrt[3]{81}}{\sqrt[3]{3}}$

Possible Answers:

$\sqrt[3]{\frac{81}{3}}= \sqrt[3]{27}= 3$

$\frac{\sqrt[3]{81}}{\sqrt[3]{3}} = \frac{3}{1}= 3$

$\sqrt[3]{81\star 3}= \sqrt[3]{243} = 6.24$

$\frac{81}{3}= 27$

$\frac{\sqrt[3]{9\star 9}}{\sqrt[3]{9}}= \sqrt[3]{9}$

Correct answer:

$\sqrt[3]{\frac{81}{3}}= \sqrt[3]{27}= 3$

Explanation:

$\frac{\sqrt[3]{81}}{\sqrt[3]{3}} = \sqrt[3]{\frac{81}{3}}= \sqrt[3]{27}= 3$

Report an Error

Example Question #2411 : Sat Mathematics

Rationalize the denominator:

$\frac{1}{2-\sqrt{3}}$

Possible Answers:

$2-\sqrt{3}$

$\sqrt{3}$

$2+\sqrt{3}$

$\frac{2+\sqrt{3}}{7}$

Correct answer:

$2+\sqrt{3}$

Explanation:

The conjugate of $2-\sqrt{3}$ is $2+\sqrt{3}$ .

Now multiply both the numerator and the denominator by $2+\sqrt{3}$

and you get:

$\frac{2+\sqrt{3}}\left ({2-\sqrt{3}} \right )\left ( 2+\sqrt{3} \right )$

$\left ( 2-\sqrt{3} \right )\left ( 2+\sqrt{3} \right ) =2^{2}-\left ( \sqrt{3} \right )^{2} =4-3 = 1$

Hence we get

$\frac{2+\sqrt{3}}{1} = 2+\sqrt{3}$

Report an Error

Example Question #11 : Exponents And Rational Numbers

Solve for :

$3^{x-5} = \frac{1}{27}$

Possible Answers:

Correct answer:

Explanation:

$3^{x-5}=\frac{1}{27}=3^{-3}$

x-5=-3

x=2

Report an Error

Example Question #4 : How To Find A Rational Number From An Exponent

Solve for .

$\log _{5}x=2$

Possible Answers:

125

Correct answer:

Explanation:

$log_5{x} = 2$

$x = 5^{2} = 25$

Report an Error

Example Question #11 : Exponential Ratios And Rational Numbers

If,

$log_a{120}= log_b{120}$

What does a=?

Possible Answers:

ab=10

$\frac{a}{b}= 120$

b=10

a=10

a=b

Correct answer:

a=b

Explanation:

If $log_a{x} = log_b{x}$ ,

then a=b .

Report an Error

Example Question #6 : How To Find A Rational Number From An Exponent

$\sqrt{x+3} -x = 1$

Possible Answers:

x=0

x=9

x=13

x=1

x=4

Correct answer:

x=1

Explanation:

From the equation in the problem statement

$\sqrt{x+3} = x + 1$

Now squaring both sides we get

$x+3=x^{2}+2x+1$ this is a quadratic equation which equals

$x^{2}+x -2 = 0$

and the factors of this equation are

$\left ( x+2 \right )\left ( x-1 \right )$

This gives us $x=-2\ or\ x=1$ .

However, if we plug these solutions back into the original equation, does not create an equality. Therefore, x=-2 is an extraneous solution.

Report an Error

Example Question #7 : How To Find A Rational Number From An Exponent

For some positive integer , if x^3=27 , what is the value of (x+2)^3 ?

Possible Answers:

125

Correct answer:

125

Explanation:

If x^3=27 , then must equal 3 (Note that cannot be -3 because you need it to be positive.

Now, plug x=3 into the new equation (x+2)^3 :

=(3+2)^3

=5^3

=125

Report an Error

View PSAT Mathematics Tutors

Chase
Certified Tutor

University of Memphis, Bachelor in Arts, Psychology.

View PSAT Mathematics Tutors

Zachary
Certified Tutor

Yale University, Bachelor of Science, Biology, General.

View PSAT Mathematics Tutors

Shakeel
Certified Tutor

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Statistics Tutors in Miami, Calculus Tutors in San Francisco-Bay Area, Statistics Tutors in Phoenix, Biology Tutors in Denver, Spanish Tutors in Dallas Fort Worth, SAT Tutors in New York City, LSAT Tutors in New York City, French Tutors in Houston, Chemistry Tutors in Philadelphia, SAT Tutors in San Diego

Popular Courses & Classes

ACT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Boston, ISEE Courses & Classes in Washington DC, LSAT Courses & Classes in Atlanta, SAT Courses & Classes in Los Angeles, LSAT Courses & Classes in Philadelphia, SAT Courses & Classes in Phoenix, SAT Courses & Classes in Boston, SSAT Courses & Classes in Los Angeles, MCAT Courses & Classes in Seattle

Popular Test Prep

GMAT Test Prep in Denver, SSAT Test Prep in Seattle, ACT Test Prep in San Francisco-Bay Area, GRE Test Prep in San Diego, LSAT Test Prep in Denver, GRE Test Prep in Philadelphia, ACT Test Prep in Los Angeles, ACT Test Prep in San Diego, GMAT Test Prep in Chicago, ACT Test Prep in Chicago

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

PSAT Math : How to find a rational number from an exponent

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1201 : Psat Mathematics

Example Question #2411 : Sat Mathematics

Example Question #11 : Exponents And Rational Numbers

Example Question #4 : How To Find A Rational Number From An Exponent

Example Question #11 : Exponential Ratios And Rational Numbers

Example Question #6 : How To Find A Rational Number From An Exponent

Example Question #7 : How To Find A Rational Number From An Exponent

All PSAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: