We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

SAT Math : Exponents

Study concepts, example questions & explanations for SAT Math

Create An Account

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #41 : Exponents

Simplify into base .

32^1*8^4*4^2

Possible Answers:

$2^{240}$

2^7

Can't be simplified.

$2^{21}$

$2^{20}$

Correct answer:

$2^{21}$

Explanation:

We need to get them to bases of . All of those bases derive from bases of but raised to different powers. is the same as 32^1 as anything raised to the first power is the same as its base. 32=2^5 .

Next, 8=2^3 . Since it's raised to the fourth power, let's make a proportion.

$\frac{1}{3}=\frac{4}{x}$ .
The top represents the power of base . The bottom represents the power of base . When we cross-multiply, we have . So $8^4=2^{12}$ .

Finally, is the same as 2^2 . Let's do another proportion.

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

The top represents the power of base . The bottom represents the power of base .Wen we cross-mulltiply, we get . So 4^2=2^4 .

With the same bases, we can add the exponents.

We have $2^{5+12+4}=2^{21}$ .

Report an Error

Example Question #451 : Algebra

x^8 can be stated as which of the following?

Possible Answers:

3 only

1 and 3

2 and 3

1 only

2 only

Correct answer:

2 and 3

Explanation:

This will test your knowledge of a specific exponential property: $(x^a)^b = x^{ab}$ . Knowing that, 2 and 3 do come out to x^8 , while 1 comes out to only x^6 .

Report an Error

Example Question #43 : How To Multiply Exponents

Simplify:

$(x^\frac{1}{2}y^\frac{3}{2})^2$

Possible Answers:

xy^3

$x^\frac{3}{2}y^\frac{5}{2}$

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

$\frac{y^\frac{1}{2}}{x}$

Correct answer:

xy^3

Explanation:

When an exponent is raised to the power of another exponent, we multiply the exponents together.

For our x-value, the exponent will be $\frac{1}{2}\cdot 2 =1$

For our y-value, the exponent will be $\frac{3}{2}\cdot 2=3$

Therefore,

$(x^\frac{1}{2}y^\frac{3}{2})^2 = xy^3$

Report an Error

Example Question #452 : Algebra

Solve for in terms of :

$t ^{- \frac{2}{5}} = h^{10}$

Possible Answers:

$t = \frac{1}{h^{4}}$

t = 100 h

$t = \sqrt[4]{h}$

$t = \frac{1}{h^{25}}$

$t = \sqrt[25]{h}$

Correct answer:

$t = \frac{1}{h^{25}}$

Explanation:

$t ^{- \frac{2}{5}} = h^{10}$

$\left (t ^{- \frac{2}{5}} \right )^{- \frac{5} {2}} =\left ( h^{10} \right )^{- \frac{5} {2}}$

$t ^{- \frac{2}{5} \cdot \left ( - \frac{5} {2} \right )} = h^{10 \cdot \left ( - \frac{5} {2} \right )}$

$t ^{1} = h^{-25 }$

$t = \frac{1}{h^{25}}$

Report an Error

Example Question #452 : Algebra

Evaluate $6^{18}*6^{24}$

Possible Answers:

$6^{24}$

$6^{42}$

$6^{432}$

$6^{36}$

$6^{48}$

Correct answer:

$6^{42}$

Explanation:

When multiplying exponents of the same base, we just add the exponents and keep the base the same.

$6^{18}*6^{24}=6^{18+24}=6^{42}$

Report an Error

Example Question #453 : Algebra

Evaluate $7^{-5}*7^{-8}$

Possible Answers:

$7^{-10}$

$7^{16}$

$7^{-13}$

$7^{-12}$

$7^{40}$

Correct answer:

$7^{-13}$

Explanation:

When multiplying exponents of the same base, we just add the exponents and keep the base the same.

$7^{-5}*7^{-8}=7^{-5-8}=7^{-13}$

Report an Error

Example Question #454 : Algebra

Evaluate 81^8*3^9

Possible Answers:

$243^{72}$

9^9

$243^{17}$

$3^{41}$

$3^{80}$

Correct answer:

$3^{41}$

Explanation:

Although we have different bases, we know that 81=3^4. Therefore we have $(3^4)^8*3^9=3^{32}*3^9=3^{41}$ .

Report an Error

Example Question #455 : Algebra

Simplify $\frac{x+(3x)^2+(2x)^3}{x}$

Possible Answers:

1+6x+6x^2

x+9x^2+8x^3

$\frac{1+9x+8x^2}{x}$

1+9x+8x^2

x+9x+8x^2

Correct answer:

1+9x+8x^2

Explanation:

Simplify the numerator

$\frac{x+(3x)^2+(2x)^3}{x}=\frac{x+3^2x^2+2^3x^3}{x}=\frac{x+9x^2+8x^3}{x}$

Pull an x out of each term in the numerator

$\frac{x(1+9x+8x^2)}{x}$

The x in the numerator and the x in the denominator cancel

1+9x+8x^2

Report an Error

Example Question #456 : Algebra

Solve:

$x^{6}\cdot x^{12}$

Possible Answers:

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

$x^{6}$

$x^{18}$

$x^{2}$

Correct answer:

$x^{18}$

Explanation:

When multiplying expressions with the same variable, combine terms by adding the exponents, while leaving the variable unchanged. For this problem, we do that by adding 6+12, to get a new exponent of 18:

$x^{6}\cdot x^{12}=x ^{6+12}=x^{18}$

Report an Error

Example Question #457 : Algebra

Solve:

$x^{2}\cdot x$

Possible Answers:

$x^{5}$

$x^{3}$

$x^{2}$

Correct answer:

$x^{3}$

Explanation:

When multiplying expressions with the same variable, combine terms by adding the exponents, while leaving the variable unchanged. For this problem, we do that by adding 2+1, to get a new exponent of 3:

$x^{2}\cdot x=x ^{2+1}=x^{3}$

Report an Error

View SAT Mathematics Tutors

Amanda
Certified Tutor

Seattle University, Current Undergrad Student, Applied Mathematics.

View SAT Mathematics Tutors

Sharif
Certified Tutor

NCCU, Bachelors, Physics and Mathematics.

View SAT Mathematics Tutors

Joy
Certified Tutor

Boston University, Bachelor in Arts, Conservation Biology.

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

SAT Math Tutors in Top Cities:

Atlanta SAT Math Tutors, Austin SAT Math Tutors, Boston SAT Math Tutors, Chicago SAT Math Tutors, Dallas Fort Worth SAT Math Tutors, Denver SAT Math Tutors, Houston SAT Math Tutors, Kansas City SAT Math Tutors, Los Angeles SAT Math Tutors, Miami SAT Math Tutors, New York City SAT Math Tutors, Philadelphia SAT Math Tutors, Phoenix SAT Math Tutors, San Diego SAT Math Tutors, San Francisco-Bay Area SAT Math Tutors, Seattle SAT Math Tutors, St. Louis SAT Math Tutors, Tucson SAT Math Tutors, Washington DC SAT Math Tutors

Popular Courses & Classes

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

Popular Test Prep

SAT Test Prep in Houston, GMAT Test Prep in Miami, SSAT Test Prep in Dallas Fort Worth, MCAT Test Prep in Chicago, LSAT Test Prep in Denver, GRE Test Prep in Los Angeles, MCAT Test Prep in Washington DC, ACT Test Prep in Houston, ACT Test Prep in Boston, SAT Test Prep in San Francisco-Bay Area

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

SAT Math : Exponents

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #41 : Exponents

Example Question #451 : Algebra

Example Question #43 : How To Multiply Exponents

Example Question #452 : Algebra

Example Question #452 : Algebra

Example Question #453 : Algebra

Example Question #454 : Algebra

Example Question #455 : Algebra

Example Question #456 : Algebra

Example Question #457 : Algebra

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: