We are open Saturday and Sunday!

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 Create Tests & Flashcards

Home Embed

All PSAT Math Resources

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

Example Questions

Example Question #2411 : Sat Mathematics

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

Possible Answers:

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

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

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

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

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

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 #11 : Exponents And Rational Numbers

Rationalize the denominator:

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

Possible Answers:

$\sqrt{3}$

$2+\sqrt{3}$

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

$2-\sqrt{3}$

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 #2413 : Sat Mathematics

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 #2421 : Sat Mathematics

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 #2422 : Sat Mathematics

If,

$log_a{120}= log_b{120}$

What does a=?

Possible Answers:

b=10

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

a=10

ab=10

a=b

Correct answer:

a=b

Explanation:

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

then a=b .

Report an Error

Example Question #231 : Exponents

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

Possible Answers:

x=1

x=4

x=13

x=0

x=9

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 #1201 : Psat Mathematics

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

Laura
Certified Tutor

Towson University, Bachelor of Science, Elementary School Teaching. University of Phoenix-Online Campus, Masters in Education...

View PSAT Mathematics Tutors

Ava
Certified Tutor

Fordham University, Bachelor in Arts, Philosophy.

View PSAT Mathematics Tutors

Robert
Certified Tutor

Drexel University, Bachelor of Science, Psychology. University of Pennsylvania, Masters, Psychology.

All PSAT Math Resources

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

Popular Subjects

GMAT Tutors in Houston, Math Tutors in Boston, LSAT Tutors in Boston, GMAT Tutors in Miami, ISEE Tutors in Houston, Statistics Tutors in Chicago, GMAT Tutors in Washington DC, Biology Tutors in Dallas Fort Worth, Algebra Tutors in Washington DC, GRE Tutors in Seattle

Popular Courses & Classes

GMAT Courses & Classes in Miami, GRE Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Seattle, GMAT Courses & Classes in New York City, GRE Courses & Classes in Boston, LSAT Courses & Classes in Miami, SAT Courses & Classes in Washington DC, ACT Courses & Classes in Houston, Spanish Courses & Classes in Chicago, ISEE Courses & Classes in Boston

Popular Test Prep

SAT Test Prep in San Diego, GMAT Test Prep in San Diego, ACT Test Prep in Houston, SAT Test Prep in Chicago, GRE Test Prep in Washington DC, ISEE Test Prep in Boston, ISEE Test Prep in Seattle, SSAT Test Prep in San Diego, MCAT Test Prep in Philadelphia, ISEE Test Prep in Miami

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 #2411 : Sat Mathematics

Example Question #11 : Exponents And Rational Numbers

Example Question #2413 : Sat Mathematics

Example Question #2421 : Sat Mathematics

Example Question #2422 : Sat Mathematics

Example Question #231 : Exponents

Example Question #1201 : Psat Mathematics

All PSAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

FIND THE BEST TUTORS

Email address:
Your name:

Email address:
Your name:
Feedback: