We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Math : Exponents

Study concepts, example questions & explanations for ISEE Upper Level Math

Create An Account

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 5 6 7 Next →

Example Question #22 : How To Divide Exponents

Simplify the following expression:

$\frac{16r^{19}}{8r^6}$

Possible Answers:

$2r^{\frac{19}{6}}$

$2r^{13}$

$8r^{13}$

2r^5

Correct answer:

$2r^{13}$

Explanation:

Simplify the following expression:

$\frac{16r^{19}}{8r^6}$

To solve this question, we need to recall that when dividing exponents we subtract them.

When dividing coefficients, we treat them as regular division.

In this case, we can break up our question into two parts:

$\frac{16r^{19}}{8r^6}\rightarrow\frac{16}{8} \frac{r^{19}}{r^6}$

The coefficients will simply reduce to "2", because 16 divided by 8 is two

The r's are another story. We subtract, so we will get the following:

$\frac{r^{19}}{r^6}=r^{19-6}=r^{13}$

So, if we put our two parts back together, we get:

$2r^{13}$

Report an Error

Example Question #101 : Numbers And Operations

Simplify the following:

$\frac{18t^6u^{14}}{6t^3u^{12}}$

Possible Answers:

3t^3u^3

3t^3u^2

3t^2u^2

12t^3u^2

Correct answer:

3t^3u^2

Explanation:

Simplify the following:

$\frac{18t^6u^{14}}{6t^3u^{12}}$

Let's begin by recalling that when dividing variables with similar base, we need to subtract the exponents.

To deal with the coefficients, simply treat them as a fraction and simplify.

$\frac{18t^6u^{14}}{6t^3u^{12}}=\frac{18}{6}t^{6-3}u^{14-12}=3t^3u^2$

So our answer is

3t^3u^2

Report an Error

Example Question #101 : Numbers And Operations

Simplify the expression:

$6x^{4} + 8x^{3} - 4x^{2}$

Possible Answers:

$10x^{5}$

$6x^{4} + 4x$

$2x^{2}(3x^{2}+4x-2)$

$6x^{4} + 4x^{5}$

$10x^{9}$

Correct answer:

$2x^{2}(3x^{2}+4x-2)$

Explanation:

$6x^{4} + 8x^{3} - 4x^{2}$

$=2x^{2}(3x^{2}+4x-2)$

Report an Error

Example Question #541 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Simplify:

4x^2+8x^3+16x^2+4x^3

Possible Answers:

4x^2(5+x)

4x^2(5+3x)

4x^2(5+3x^2)

4x(5+3x)

x^2(5+3x)

Correct answer:

4x^2(5+3x)

Explanation:

In order to add exponential terms, both the base and the exponent must be the same. So we can write:

4x^2+8x^3+16x^2+4x^3=(4x^2+16x^2)+(8x^3+4x^3)

=20x^2+12x^3=4x^2(5+3x)

Report an Error

Example Question #3 : How To Add Exponents

Evaluate:

$\frac{x^0+y^0+1}{x^0-y^0-1}$

Possible Answers:

Correct answer:

Explanation:

Based on the zero-exponent rule we have:

a^0=1

That means any non-zero number raised to the zero power is equal to . So we can write:

$\frac{1+1+1}{1-1-1}=\frac{3}{-1}=-3$

Report an Error

Example Question #102 : Numbers And Operations

What is the value of the expression:

$x^{3}\cdotx^{y}\cdot x^{2+y}$

Possible Answers:

$x^{4}\cdotx^{y+4}$

$x^{3}\cdotx^{y+2}$

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

$x^{6}\cdotx^{y+2}$

Correct answer:

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

Explanation:

When values, having the same base, are multiplied by one another, the exponents are added together and the base stays the same.

Thus,

$x^{3}\cdotx^{y}\cdot x^{2+y}$

is equal to

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

Report an Error

Example Question #103 : Numbers And Operations

Simplify: $x^{7}\cdot2x^{3}$

Possible Answers:

$x^{21}$

$x^{10}$

$2x^{10}$

$2x^{21}$

Correct answer:

$2x^{10}$

Explanation:

When multiplying exponents, the exponents are added together. Thus, 3 and 7 are added together for a sum of 10. In this problem, the "2" becomes a coefficient in front of the x. Therefore, the correct answer is:

$2x^{10}$

Report an Error

Example Question #111 : Numbers And Operations

Simplify:

$x^{6}\cdot x^{4}$

Possible Answers:

$x^{-2}$

$x^{-10}$

$x^{24}$

$x^{2}$

$x^{10}$

Correct answer:

$x^{10}$

Explanation:

When multiplying exponents, the exponents are added together.

$x^{6}\cdot x^{4} = x^{6+4}=x^{10}$

Report an Error

Example Question #112 : Numbers And Operations

Simplify:

$2x^{2}\cdot 3x^{4}$

Possible Answers:

$6x^{8}$

$6x^{6}$

$6x^{2}$

$5x^{6}$

$\frac{2}{3}x^{6}$

Correct answer:

$6x^{6}$

Explanation:

When multiplying exponents, the exponents are added together.

$2x^{2}\cdot 3x^{4}=6x^{2+4}=6x^{6}$

Report an Error

Example Question #1 : How To Add Exponents

Simplify the expression:

$3x^{4}+6x^{3}-9x^{2}$

Possible Answers:

$3x(x^{2}+3x-3)$

$3x^{2}(x^{2}+2x-3)$

$3x^{2}(x^{2}+2x-3x)$

$3x(x^{2}+2x-3)$

$2x^{2}(x^{2}+2x-3x)$

Correct answer:

$3x^{2}(x^{2}+2x-3)$

Explanation:

To simplify this problem we need to factor out a 3x^2

$3x^{4}+6x^{3}-9x^{2}$

$=3x^{2}(x^{2}+2x-3)$

We can do this because multiplying exponents is the same as adding them. Therefore,

$=3x^{2}(x^{2}+2x-3)$

$=3x^2 \cdot x^2 +3x^2\cdot2x -3x^2\cdot3=3x^{2+2}+3\cdot2x^{2+1}-3\cdot 3x^2$

=3x^4+6x^3-9x^2

Report an Error

← Previous 1 2 3 4 5 6 7 Next →

View Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

View Tutors

Lazaro
Certified Tutor

Miami Dade College, Bachelor of Engineering, Computer Hardware Engineering.

View Tutors

Jaskaran
Certified Tutor

University of Windsor, Master's/Graduate, Computer science.

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Reading Tutors in Seattle, Chemistry Tutors in Houston, GMAT Tutors in Phoenix, Biology Tutors in New York City, ACT Tutors in Seattle, Math Tutors in Denver, Algebra Tutors in Dallas Fort Worth, ACT Tutors in Atlanta, ACT Tutors in Dallas Fort Worth, English Tutors in New York City

Popular Courses & Classes

ACT Courses & Classes in Philadelphia, MCAT Courses & Classes in Chicago, GRE Courses & Classes in New York City, Spanish Courses & Classes in Seattle, SSAT Courses & Classes in Atlanta, ACT Courses & Classes in Seattle, LSAT Courses & Classes in Philadelphia, MCAT Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Boston, LSAT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

ISEE Test Prep in Atlanta, SAT Test Prep in Denver, SAT Test Prep in Dallas Fort Worth, ACT Test Prep in Denver, SSAT Test Prep in Dallas Fort Worth, SSAT Test Prep in Washington DC, ACT Test Prep in Philadelphia, LSAT Test Prep in Houston, SSAT Test Prep in Phoenix, ISEE Test Prep in Dallas Fort Worth

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

ISEE Upper Level Math : Exponents

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

Example Question #22 : How To Divide Exponents

Example Question #101 : Numbers And Operations

Example Question #101 : Numbers And Operations

Example Question #541 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #3 : How To Add Exponents

Example Question #102 : Numbers And Operations

Example Question #103 : Numbers And Operations

Example Question #111 : Numbers And Operations

Example Question #112 : Numbers And Operations

Example Question #1 : How To Add Exponents

All ISEE Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: