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

← Previous 1 2 … 5 6 7 8 9 10 11 12 13 … 28 29 Next →

Example Question #81 : Exponents

What is the value of such that 2^n=4^2*16^3*32^2 ?

Possible Answers:

240

480

Correct answer:

Explanation:

We can solve by converting all terms to a base of two. 4, 16, and 32 can all be expressed in terms of 2 to a standard exponent value.

$4=2^2\rightarrow 4^2=(2^2)^2$

$16=2^4\rightarrow 16^3=(2^4)^3$

$32=2^5\rightarrow 32^2=(2^5)^2$

We can rewrite the original equation in these terms.

2^n=(2^2)^2*(2^4)^3*(2^5)^2

Simplify exponents.

$2^n=(2^4)*(2^{12})*(2^{10})$

Finally, combine terms.

$2^n=2^{4+12+10}=2^{26}$

From this equation, we can see that n=26 .

Report an Error

Example Question #82 : Exponents

Solve for $x$ :

$4^{4}+4^{4}+4^{4}+4^{4}=2^{x}$

Possible Answers:

$9$

$10$

$6$

$11$

$8$

Correct answer:

$10$

Explanation:

Combining the powers, we get $1024=2^{x}$ .

From here we can use logarithms, or simply guess and check to get $x=10$ .

Report an Error

Example Question #83 : Exponents

Simplify:

$x^{4}\cdot x^{5}$

Possible Answers:

$x^{10}$

$x^{9}$

$x^{7}$

$x^{2}$

Correct answer:

$x^{9}$

Explanation:

When multiplying exponents with the same base, we use the rules of exponents.

This means you must simply add the exponents together as shown below:

$x^{4}\cdot x^{5} = x^{4+5} = x^{9}$

Report an Error

Example Question #4 : How To Add Exponents

Simplify: y³x⁴(yx³ + y²x² + y¹⁵ + x²²)

Possible Answers:

2x⁴y⁴ + 7y¹⁵ + 7x²²

y⁴x⁷ + y⁵x⁶ + y¹⁸x⁴ + y³x²⁶

y³x¹² + y⁶x⁸ + y⁴⁵ + x⁸⁸

y³x¹² + y¹²x⁸ + y²⁴x⁴ + y³x²³

y³x¹² + y⁶x⁸ + y⁴⁵x⁴ + y³x⁸⁸

Correct answer:

y⁴x⁷ + y⁵x⁶ + y¹⁸x⁴ + y³x²⁶

Explanation:

When you multiply exponents, you add the common bases:

y⁴ x⁷ + y⁵x⁶ + y¹⁸x⁴ + y³x²⁶

Report an Error

Example Question #6 : Exponential Operations

If $\frac{3^{y - 1}}{3^{-2}} = 27^{y}3^{y}$ , what is the value of ?

Possible Answers:

$\frac{2}{3}$

$\frac{3}{2}$

$\frac{1}{3}$

Correct answer:

$\frac{1}{3}$

Explanation:

Rewrite the term on the left as a product. Remember that negative exponents shift their position in a fraction (denominator to numerator).

$3^{y-1}*3^2=27^y3^y$

The term on the right can be rewritten, as 27 is equal to 3 to the third power.

$3^{y-1}*3^2=(3^3)^y*3^y$

Exponent rules dictate that multiplying terms allows us to add their exponents, while one term raised to another allows us to multiply exponents.

$3^{(y-1)+2}=(3)^{3y}*3^y$

$3^{y+1}=3^{3y+y}=3^{4y}$

We now know that the exponents must be equal, and can solve for .

y+1=4y

1=3y

$\frac{1}{3}=y$

Report an Error

Example Question #11 : Exponential Operations

If $5^2 \times 5^n = 5^{12}$ , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

Since the base is 5 for each term, we can say 2 + n =12. Solve the equation for n by subtracting 2 from both sides to get n = 10.

Report an Error

Example Question #84 : Exponents

Simplify: $3^2\times3^3\times3^{-4}$

Possible Answers:

$\frac{1}{3}$

$\frac{1}{9}$

Correct answer:

Explanation:

To determine the value of this expression, it is not necessary to determine the values of each term's power. Instead, since these powers have the same bases and are multiplied, the powers can be added.

$3^2\times3^3\times3^{-4} = 3^{2+3+(-4)} = 3^1=3$

The answer is .

Report an Error

Example Question #85 : Exponents

If $y = 5^{a} * 5^{b}$ and a + b = 3 , what is the value of ?

Possible Answers:

125

150

Correct answer:

125

Explanation:

Multiplying two exponents that have the same base is the equivalent of simply adding the exponents.

So $y = 5^{a} * 5^{b}$ is the same as $y = 5^{a + b}$ , and if a + b = 3 , then $y = 5^{3}$ or 125 .

Report an Error

Example Question #86 : Exponents

Evaluate: 3^x+9^x

Possible Answers:

12^x

$3^{3x}$

$3^x+3^{2x}$

$3^{x^2}$

Correct answer:

$3^x+3^{2x}$

Explanation:

The exponents cannot be added unless the both bases are alike and similar bases must be multiplied with each other. Rewrite the nine with a base of three.

9=3^2

Rewrite the expression.

$3^x+9^x= 3^x+3^{2x}$

Do not add the exponents, since similar bases are added and are not multiplied with each other!

The answer is: $3^x+3^{2x}$

Report an Error

Example Question #81 : Exponential Operations

Simplify:

$x^5y^4z^2 \cdot x^4y^5z^2$

Possible Answers:

x^9y^9z^4

$xy^{-1}$

$\frac{x^5y^4z^2 }{x^4y^5z^2}$

$x^{20}y^{20}z^{4}$

Correct answer:

x^9y^9z^4

Explanation:

When we multiply two polynomials with exponents, we add their exponents together. Therefore,

$x^5y^4z^2 \cdot x^4y^5z^2 = x^9y^9z^4$

Report an Error

← Previous 1 2 … 5 6 7 8 9 10 11 12 13 … 28 29 Next →

View SAT Mathematics Tutors

Bill
Certified Tutor

SUNY Empire State College, Bachelors, General Sciences, Theater.

View SAT Mathematics Tutors

Stephen
Certified Tutor

Grinnell College, Bachelor in Arts, Computer Science.

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

ISEE Courses & Classes in Washington DC, GRE Courses & Classes in Chicago, ISEE Courses & Classes in Miami, MCAT Courses & Classes in Phoenix, ISEE Courses & Classes in Seattle, GMAT Courses & Classes in Seattle, GMAT Courses & Classes in Washington DC, Spanish Courses & Classes in Philadelphia, MCAT Courses & Classes in Philadelphia, ACT Courses & Classes in Miami

Popular Test Prep

ISEE Test Prep in San Francisco-Bay Area, SAT Test Prep in Atlanta, MCAT Test Prep in Philadelphia, ACT Test Prep in Miami, ISEE Test Prep in Houston, ACT Test Prep in Boston, ISEE Test Prep in San Diego, GRE Test Prep in Denver, GMAT Test Prep in Seattle, GRE Test Prep in Phoenix

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 #81 : Exponents

Example Question #82 : Exponents

Example Question #83 : Exponents

Example Question #4 : How To Add Exponents

Example Question #6 : Exponential Operations

Example Question #11 : Exponential Operations

Example Question #84 : Exponents

Example Question #85 : Exponents

Example Question #86 : Exponents

Example Question #81 : Exponential Operations

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: