Call Now to Set Up Tutoring:

(888) 888-0446

SAT Math : How to find patterns in 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 #2 : Pattern Behaviors In Exponents

If a^x·a⁴ = a¹² and (b^y)³ = b¹⁵, what is the value of x - y?

Possible Answers:

-4

-9

-2

Correct answer:

Explanation:

Multiplying like bases means add the exponents, so x+4 = 12, or x = 8.

Raising a power to a power means multiply the exponents, so 3y = 15, or y = 5.

x - y = 8 - 5 = 3.

Report an Error

Example Question #1 : How To Find Patterns In Exponents

If p and q are positive integrers and 27^p= 9^q, then what is the value of q in terms of p?

Possible Answers:

(3/2)p

(2/3)p

Correct answer:

(3/2)p

Explanation:

The first step is to express both sides of the equation with equal bases, in this case 3. The equation becomes 3^3p= 3^2q. So then 3p = 2q, and q = (3/2)p is our answer.

Report an Error

Example Question #2 : How To Find Patterns In Exponents

Simplify 27^2/3.

Possible Answers:

125

729

Correct answer:

Explanation:

27^2/3 is 27 squared and cube-rooted. We want to pick the easier operation first. Here that is the cube root. To see that, try both operations.

27^2/3 = (27²)^1/3 = 729^1/3 OR

27^2/3 = (27^1/3)² = 3²

Obviously 3² is much easier. Either 3² or 729^1/3 will give us the correct answer of 9, but with 3² it is readily apparent.

Report an Error

Example Question #3 : How To Find Patterns In Exponents

If and are integers and

$\left ( \frac{1}{3} \right )^{a}=27^{b}$

what is the value of $a\div b$ ?

Possible Answers:

$-\frac{1}{3}$

$\frac{1}{3}$

Correct answer:

Explanation:

To solve this problem, we will have to take the log of both sides to bring down our exponents. By doing this, we will get $\dpi{100} \small a\ast log\left (\frac{1}{3} \right )= b\ast log\left ( 27 \right )$ .

To solve for $\dpi{100} \small \frac{a}{b}$ we will have to divide both sides of our equation by $\dpi{100} \small log\frac{1}{3}$ to get $\dpi{100} \small \frac{a}{b}=\frac{log\left ( 27 \right )}{log\left ( \frac{1}{3} \right )}$ .

$\dpi{100} \small \frac{log\left ( 27 \right )}{log\left ( \frac{1}{3} \right )}$ will give you the answer of –3.

Report an Error

Example Question #4 : How To Find Patterns In Exponents

If $\log 2=0.301$ and $\log 3=0.477$ , then what is $\log 12$ ?

Possible Answers:

1.592

1.116

1.255

1.079

1.346

Correct answer:

1.079

Explanation:

We use two properties of logarithms:

$log(xy) = log (x) + log (y)$

$log(x^{n}) = nlog (x)$

So $\log 12=2 \log2+\log3$

Report an Error

Example Question #571 : Algebra

Evaluate:

$x^{-3}x^{6}$

Possible Answers:

$x^{6}$

$x^{9}$

$x^{-3}$

$x^{3}$

$x^{-18}$

Correct answer:

$x^{3}$

Explanation:

$x^{m}\ast x^{n} = x^{m + n}$ , here m=-3 and n=6 , hence -3+6=3 .

Report an Error

Example Question #5 : How To Find Patterns In Exponents

Solve for

$\left ( \frac{2}{3} \right )^{x+1} = \frac{27}{8}$

Possible Answers:

None of the above

Correct answer:

Explanation:

$\left ( \frac{2}{3} \right )^{x+1} = \frac{27}{8}$ = $\left ( \frac{3}{2} \right )^{3} = \left ( \frac{2}{3} \right )^{-3}$

x+1=-3 which means x=-4

Report an Error

Example Question #6 : How To Find Patterns In Exponents

Which of the following statements is the same as:

$\dfrac{4^{x+2}}{2^y}$

$I)\ 2^{2x+4-y} \quad II)\ 2^{x+2} / 4^y \quad III)\ (4^x)( 4^2 )(2^{-y} )$

Possible Answers:

$I \mbox{ and } II \mbox{ only}$

$I \mbox{ only}$

$I \mbox{ and } III \mbox{ only}$

$I, II \mbox{ and } III$

$II \mbox{ and } III \mbox{ only}$

Correct answer:

$I \mbox{ and } III \mbox{ only}$

Explanation:

Remember the laws of exponents. In particular, when the base is nonzero:

$b^{m+n} = b^m b^n \qquad (b^m)^n = b^{mn} \\ (b \times c)^n = b^n c^n \qquad b^{-n} = 1/b^n$

An effective way to compare these statements, is to convert them all into exponents with base 2. The original statement becomes:

$4^{x+2} / 2^y = 4^{x+2} (2^{-y}) = (2^2)^{x+2} 2^{-y} = 2^{2(x+2) } 2^{-y} = 2^{2x+4-y}$

This is identical to statement I. Now consider statement II:

$2^{x+2} / 4^y = 2^{x+2} ( 4^{-y} ) = 2^{x+2} ( 2^2 )^{-y} = 2^{x+2} 2^{-2y} = 2^{x+2-2y} \neq 2^{2x+4-y}$

Therefore, statement II is not identical to the original statement. Finally, consider statement III:

$(4^x)(4^2 ) (2^{-y}) = (2^2)^x (2^2)^2 (2^{-y}) = (2^{2x} )( 2^4 ) (2^{-y}) = 2^{2x+4-y}$

which is also identical to the original statement. As a result, only I and III are the same as the original statement.

Report an Error

Example Question #7 : How To Find Patterns In Exponents

Write in exponential form:

$\sqrt[3]{\left ( x-1 \right )^{2}}$

Possible Answers:

$\left ( x-1 \right )^{\frac{2}{3}}$

$\left ( x-1 \right )^{\frac{3}{2}}$

$\left ( x-1 \right )^{2}$

$\left ( x-1 \right )$

$\left ( x-1 \right )^{3}$

Correct answer:

$\left ( x-1 \right )^{\frac{2}{3}}$

Explanation:

Using properties of radicals e.g., $\sqrt[m]{x^{n}} = x^{\frac{n}{m}}$

we get $\sqrt[3]{\left ( x-1 \right )^{2}} = \left ( x-1 \right )^{\frac{2}{3}}$

Report an Error

Example Question #261 : Exponents

Write in exponential form:

$\sqrt[3]{x^{5}}$

Possible Answers:

$x^{5-3}$

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

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

$x^{5}$

$x^{3}$

Correct answer:

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

Explanation:

Properties of Radicals

$\sqrt[]{x} = x^{\frac{1}{2}}$

$\sqrt[3]{x} = x^{\frac{1}{3}}$

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

Report an Error

View SAT Mathematics Tutors

Priyanka
Certified Tutor

CUNY Hunter College, Bachelor in Arts, Economics.

View SAT Mathematics Tutors

Karen
Certified Tutor

Bradley University, Bachelor of Science, Multimedia with a minor in Business Administration.

View SAT Mathematics Tutors

Stephen
Certified Tutor

Grinnell College, Bachelor in Arts, Computer Science.

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

ACT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Houston, ISEE Courses & Classes in New York City, GMAT Courses & Classes in Los Angeles, GRE Courses & Classes in Denver, LSAT Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Los Angeles, MCAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Seattle, SAT Courses & Classes in Chicago

Popular Test Prep

ISEE Test Prep in Atlanta, ISEE Test Prep in New York City, GMAT Test Prep in Chicago, SAT Test Prep in Miami, ISEE Test Prep in Miami, SAT Test Prep in Phoenix, ACT Test Prep in Boston, GRE Test Prep in Boston, SSAT Test Prep in Miami, LSAT 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 : How to find patterns in exponents

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #2 : Pattern Behaviors In Exponents

Example Question #1 : How To Find Patterns In Exponents

Example Question #2 : How To Find Patterns In Exponents

Example Question #3 : How To Find Patterns In Exponents

Example Question #4 : How To Find Patterns In Exponents

Example Question #571 : Algebra

Example Question #5 : How To Find Patterns In Exponents

Example Question #6 : How To Find Patterns In Exponents

Example Question #7 : How To Find Patterns In Exponents

Example Question #261 : Exponents

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: