Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Math : Exponential Operations

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

Example Question #102 : Numbers And Operations

Simplify the following expression:

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

Possible Answers:

2r^5 $\displaystyle 2r^5$

$2r^{13}$ $\displaystyle 2r^{13}$

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

$8r^{13}$ $\displaystyle 8r^{13}$

Correct answer:

$2r^{13}$ $\displaystyle 2r^{13}$

Explanation:

Simplify the following expression:

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

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:

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

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:

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

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

$2r^{13}$ $\displaystyle 2r^{13}$

Report an Error

Example Question #103 : Numbers And Operations

Simplify the following:

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

Possible Answers:

3t^3u^2 $\displaystyle 3t^3u^2$

3t^2u^2 $\displaystyle 3t^2u^2$

$\displaystyle 12t^3u^2$

3t^3u^3 $\displaystyle 3t^3u^3$

Correct answer:

3t^3u^2 $\displaystyle 3t^3u^2$

Explanation:

Simplify the following:

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

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.

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

So our answer is

3t^3u^2 $\displaystyle 3t^3u^2$

Report an Error

Example Question #51 : Exponential Operations

Simplify the expression:

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

Possible Answers:

$6x^{4} + 4x$ $\displaystyle 6x^{4} + 4x$

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

$10x^{9}$ $\displaystyle 10x^{9}$

$10x^{5}$ $\displaystyle 10x^{5}$

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

Correct answer:

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

Explanation:

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

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

Report an Error

Example Question #52 : Exponential Operations

Simplify:

$\displaystyle 4x^2+8x^3+16x^2+4x^3$

Possible Answers:

$\displaystyle 4x(5+3x)$

$\displaystyle 4x^2(5+3x^2)$

$\displaystyle x^2(5+3x)$

$\displaystyle 4x^2(5+3x)$

$\displaystyle 4x^2(5+x)$

Correct answer:

$\displaystyle 4x^2(5+3x)$

Explanation:

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

$\displaystyle 4x^2+8x^3+16x^2+4x^3=(4x^2+16x^2)+(8x^3+4x^3)$

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

Report an Error

Example Question #55 : Exponents

Evaluate:

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

Possible Answers:

$\displaystyle 1$

$\displaystyle 3$

$\displaystyle -3$

$\displaystyle 0$

$\displaystyle 2$

Correct answer:

$\displaystyle -3$

Explanation:

Based on the zero-exponent rule we have:

a^0=1 $\displaystyle a^0=1$

That means any non-zero number raised to the zero power is equal to $\displaystyle 1$. So we can write:

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

Report an Error

Example Question #3 : How To Add Exponents

What is the value of the expression:

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

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

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

Thus,

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

is equal to

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

Report an Error

Example Question #4 : How To Add Exponents

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

Possible Answers:

$x^{21}$ $\displaystyle x^{21}$

$x^{10}$ $\displaystyle x^{10}$

$2x^{10}$ $\displaystyle 2x^{10}$

$2x^{21}$ $\displaystyle 2x^{21}$

Correct answer:

$2x^{10}$ $\displaystyle 2x^{10}$

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:

$2x^{10}$ $\displaystyle 2x^{10}$

Report an Error

Example Question #5 : How To Add Exponents

Simplify:

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

Possible Answers:

$x^{2}$ $\displaystyle x^{2}$

$x^{24}$ $\displaystyle x^{24}$

$x^{10}$ $\displaystyle x^{10}$

$x^{-2}$ $\displaystyle x^{-2}$

$x^{-10}$ $\displaystyle x^{-10}$

Correct answer:

$x^{10}$ $\displaystyle x^{10}$

Explanation:

When multiplying exponents, the exponents are added together.

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

Report an Error

Example Question #6 : How To Add Exponents

Simplify:

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

Possible Answers:

$5x^{6}$ $\displaystyle 5x^{6}$

$6x^{6}$ $\displaystyle 6x^{6}$

$6x^{8}$ $\displaystyle 6x^{8}$

$6x^{2}$ $\displaystyle 6x^{2}$

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

Correct answer:

$6x^{6}$ $\displaystyle 6x^{6}$

Explanation:

When multiplying exponents, the exponents are added together.

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

Report an Error

Example Question #60 : Exponents

Simplify the expression:

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

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

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

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

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

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

$\displaystyle =3x^4+6x^3-9x^2$

Report an Error

View Tutors

Ana
Certified Tutor

Grand Canyon University, Bachelors, Education. Grand Canyon University, Masters, Education.

View Tutors

John
Certified Tutor

The University of Texas at Arlington, Bachelor of Science, Mathematics. Stanford University, Master of Science, Aerospace Eng...

View Tutors

Ebenezer
Certified Tutor

McGill University, Master of Science, Electrical Engineering.

All ISEE Upper Level Math Resources

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

Popular Subjects

Computer Science Tutors in San Francisco-Bay Area, Reading Tutors in Los Angeles, Chemistry Tutors in Seattle, Statistics Tutors in Atlanta, ACT Tutors in Philadelphia, LSAT Tutors in Miami, LSAT Tutors in Denver, French Tutors in Philadelphia, GRE Tutors in Atlanta, French Tutors in Atlanta

Popular Courses & Classes

MCAT Courses & Classes in Miami, LSAT Courses & Classes in New York City, ISEE Courses & Classes in Philadelphia, Spanish Courses & Classes in Boston, LSAT Courses & Classes in Boston, SSAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Philadelphia, SAT Courses & Classes in Houston, LSAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Los Angeles

Popular Test Prep

SAT Test Prep in New York City, GMAT Test Prep in Philadelphia, SAT Test Prep in Houston, ACT Test Prep in Houston, SSAT Test Prep in Los Angeles, SSAT Test Prep in Miami, MCAT Test Prep in New York City, SSAT Test Prep in Phoenix, LSAT Test Prep in Phoenix, SSAT Test Prep in New York City

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 : Exponential Operations

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #102 : Numbers And Operations

Example Question #103 : Numbers And Operations

Example Question #51 : Exponential Operations

Example Question #52 : Exponential Operations

Example Question #55 : Exponents

Example Question #3 : How To Add Exponents

Example Question #4 : How To Add Exponents

Example Question #5 : How To Add Exponents

Example Question #6 : How To Add Exponents

Example Question #60 : 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: