We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

SAT Math : SAT Mathematics

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 #62 : Exponents

Convert the product of 16^8*2^4 to base .

Possible Answers:

$2^{12}$

$2^{36}$

$2^{64}$

$2^{24}$

$2^{16}$

Correct answer:

$2^{36}$

Explanation:

Although they have different bases, we know that 16=2^4 .

Therefore

$16^8=(2^4)^8=2^{32}$ .

Remember to apply the power rule of exponents.

Finally,

$2^{32}*2^4=2^{32+4}=2^{36}$ .

Report an Error

Example Question #21 : How To Multiply Exponents

Solve for :

$\sqrt[3]{x-3} = 2$

Possible Answers:

$None\ of\ the\ above$

Correct answer:

Explanation:

$\left ( \sqrt[3]{x-3} \right )^{3} = 2^{3}$

Now the left side equals x-3 and the right side equals 8. Hence:

x-3 = 8

Therefore must be equal to 11.

Report an Error

Example Question #63 : Exponents

Define an operation $\bigstar$ on the set of real numbers as follows:

For all real a,b ,

$a \bigstar b =\left ( \frac{1}{a} \right )^ {\frac{1}{b}}$

Evaluate: $81 \bigstar (-2)$ .

Possible Answers:

$\frac{1}{9}$

$\frac{1}{6,561}$

6,561

The value of $81 \bigstar (-2)$ is undefined.

Correct answer:

Explanation:

Set a =81 and b= -2 in the expression in the definition, then simplify:

$a \bigstar b =\left ( \frac{1}{a} \right )^ {\frac{1}{b}}$

$81\bigstar (-2) =\left ( \frac{1}{81} \right )^ {\frac{1}{-2}} = \left ( \frac{1}{81} \right )^ {-\frac{1}{2}}$

By definition,

$a ^{-M} = \frac{1}{a^{M}} = \frac{1^{M}}{a^{M}}= \left ( \frac{1}{a} \right )^{M}$ ;

setting N = -M ,

$\left ( \frac{1}{a} \right )^{-N} = a ^{N}$ .

Substituting a = 81 and $N = -\frac{1}{2}$ ,

$81\bigstar (-2) = \left ( \frac{1}{81} \right )^ {-\frac{1}{2}} = 81 ^ {\frac{1}{2}}$

Also, raising a number to the power of $\frac{1}{M}$ is equivalent to taking the th root of the number; specifically, raising a number to the power of $\frac{1}{2}$ is equivalent to taking its square root. Therefore,

$81\bigstar (-2) = 81 ^ {\frac{1}{2}} = \sqrt{81} = 9$ .

Report an Error

Example Question #472 : Algebra

$\sqrt[6]{x} = t$

Express $\sqrt{x}$ in terms of .

Possible Answers:

$t ^{4}$

$t^{3}$

$t \sqrt{t}$

Correct answer:

$t^{3}$

Explanation:

By definition,

$\sqrt[6]{x} = x^{\frac{1}{6}}$

and

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

By the Power of a Power Rule,

$x^{\frac{1}{2}} = x^{\frac{1}{6}\cdot 3 } = \left ( x ^{\frac{1}{6}}\right ) ^{3}$ ,

so, by substituting,

$\sqrt{x} = \left ( \sqrt[6]{x} \right ) ^{3} = t^{3}$ .

Report an Error

Example Question #63 : Exponents

Simplify the expression.

x^3(2x^2)

Possible Answers:

4x^6

2x^5

2x^6

4x^5

2x^7

Correct answer:

2x^5

Explanation:

When multiplying with exponents, you must add the exponents.

Therefore, multiply the coefficients on the x terms and add the exponents

x^3(2x^2)

$\\1x^3\cdot2x^2=2x^(3+2)=2x^5$

Report an Error

Example Question #481 : Algebra

Which of the following is equivalent to (3x^4)(2x^2)

Possible Answers:

6x^8

5x^6

6x^6

5x^8

Correct answer:

6x^6

Explanation:

and can be multiplied together to give you which is the first part of our answer. When you multiply exponents with the same base (in this case, ), you add the exponents. In this case, $x^4\times x^2$ should give us x^6 because 4+2=6 . The answer is 6x^6

Report an Error

Example Question #1 : How To Add Exponents

If a² = 35 and b² = 52 then a⁴ + b⁶ = ?

Possible Answers:

522

150,000

141,833

3929

140,608

Correct answer:

141,833

Explanation:

a⁴= a² * a² and b⁶= b² * b²* b²

Therefore a⁴ + b⁶ = 35 * 35 + 52 * 52 * 52 = 1,225 + 140,608 = 141,833

Report an Error

Example Question #2 : How To Add Exponents

Solve for x.

2³+ 2^x+1= 72

Possible Answers:

Correct answer:

Explanation:

The answer is 5.

8 + 2^x+1= 72

2^x+1= 64

2^x+1= 2⁶

x + 1 = 6

x = 5

Report an Error

Example Question #2 : Exponents

Which of the following is eqivalent to 5^b – 5^(b–1) – 5^(b–1)– 5^(b–1)– 5^(b–1)– 5^(b–1), where b is a constant?

Possible Answers:

5^b–1

1/5

Correct answer:

Explanation:

We want to simplify 5^b – 5^(b–1)– 5^(b–1)– 5^(b–1)– 5^(b–1)– 5^(b–1).

Notice that we can collect the –5⁽^b–1) terms, because they are like terms. There are 5 of them, so that means we can write –5^(b–1)– 5^(b–1)– 5^(b–1)– 5^(b–1)– 5^(b–1)as (–5^(b–1))5.

To summarize thus far:

5^b – 5^(b–1)– 5^(b–1)– 5^(b–1)– 5^(b–1)– 5^(b–1)= 5^b +(–5^(b–1))5

It's important to interpret –5^(b–1)as (–1)5^(b–1) because the –1 is not raised to the (b – 1) power along with the five. This means we can rewrite the expression as follows:

5^b +(–5^(b–1))5 = 5^b + (–1)(5^(b–1))(5) = 5^b – (5^(b–1))(5)

Notice that 5⁽^b–1) and 5 both have a base of 5. This means we can apply the property of exponents which states that, in general, a^ba^c = a^b+c. We can rewrite 5 as 5¹ and then apply this rule.

5^b – (5^(b–1))(5) = 5^b – (5^(b–1))(5¹) = 5^b – 5^(b–1+1)

Now, we will simplify the exponent b – 1 + 1 and write it as simply b.

5^b – 5^(b–1+1)= 5^b – 5^b = 0

The answer is 0.

Report an Error

Example Question #2251 : Sat Mathematics

If $x^2=11$ , then what does $x^4$ equal?

Possible Answers:

121

144

110

Correct answer:

121

Explanation:

$x^4=(x^2)(x^2)=11\cdot 11=121$

Report an Error

View SAT Mathematics Tutors

Nicholas
Certified Tutor

Fordham University, Bachelors, Business Administration and Management. Boston University, Master of Arts, Multimedia.

View SAT Mathematics Tutors

Alena
Certified Tutor

Mogilevsky State Pedagogical Institute, Bachelor in Arts, Mathematics. Mogilevsky State Pedagogical Institute, Masters, Mathe...

View SAT Mathematics Tutors

Zachary
Certified Tutor

Yale University, Bachelor of Science, Biology, General.

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

LSAT Courses & Classes in Miami, GRE Courses & Classes in Philadelphia, GRE Courses & Classes in Seattle, SAT Courses & Classes in Houston, MCAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in San Diego, LSAT Courses & Classes in Washington DC, SAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Dallas Fort Worth

Popular Test Prep

SAT Test Prep in Dallas Fort Worth, LSAT Test Prep in San Diego, GRE Test Prep in Seattle, GRE Test Prep in Miami, GMAT Test Prep in Houston, MCAT Test Prep in Chicago, GRE Test Prep in Philadelphia, MCAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Los Angeles, ACT Test Prep in Atlanta

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 : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #62 : Exponents

Example Question #21 : How To Multiply Exponents

Example Question #63 : Exponents

Example Question #472 : Algebra

Example Question #63 : Exponents

Example Question #481 : Algebra

Example Question #1 : How To Add Exponents

Example Question #2 : How To Add Exponents

Example Question #2 : Exponents

Example Question #2251 : Sat Mathematics

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: