Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Math : How to find the exponent of variables

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 Next →

Example Question #1 : How To Find The Exponent Of Variables

Simplify:

$\left (6x ^{-5 } \right )^{-3}$

Possible Answers:

$216x^{2}$

$-\frac{x^{2}}{216}$

$-18x^{15}$

$\frac{x^{15}}{216}$

$-18x^{2}$

Correct answer:

$\frac{x^{15}}{216}$

Explanation:

Apply the power of a product property:

$\left (6x ^{-5 } \right )^{-3}$

$= 6 ^{-3}\cdot \left (x ^{-5 } \right )^{-3}$

$=\frac{1}{216}\cdot x ^{-5 \cdot (-3) }$

$=\frac{1}{216}\cdot x ^{15 }$

$=\frac{x ^{15 }}{216}$

Report an Error

Example Question #2 : How To Find The Exponent Of Variables

What is the coefficient of $x^{5}$ in the expansion of $(x+1)^{12}$ .

Possible Answers:

7,920

9,504

792

Correct answer:

792

Explanation:

By the Binomial Theorem, if $(x + 1)^{n}$ is expanded, the coefficient of $x^{r}$ is

$_{n}\textrm{C} _{r} = \frac{n!}{(n-r)!r!}$ .

Substitute n = 12, r = 5 : The coefficient of $x^{5}$ is:

$_{12}\textrm{C} _{5} = \frac{12!}{(12-5)!5!} = \frac{12!}{7!5!}$

$= \frac{12 \cdot 11\cdot 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}{7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}$

$= \frac{12 \cdot 11\cdot 10\cdot 9\cdot 8}{ 5\cdot 4\cdot 3\cdot 2\cdot 1} = \frac{11\cdot 9\cdot 8}{ 1} = 792$

Report an Error

Example Question #961 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Simplify the expression: $\left [\left ( x ^{3} \right )^{3} \right ]^{3 }$

Possible Answers:

$x ^{9}$

$27x^{3}$

$x^{27}$

$x^ {18}$

729x

Correct answer:

$x^{27}$

Explanation:

Apply the power of a power property twice:

$\left [\left ( x ^{3} \right )^{3} \right ]^{3 } = ( x ^{3\; \cdot \; 3 } )^{3 } = ( x ^{9 } )^{3 } = x ^{9\cdot 3} =x ^{27}$

Report an Error

Example Question #961 : Isee Upper Level (Grades 9 12) Mathematics Achievement

What is the coefficient of $x^{4}$ in the expansion of $(2x + 3)^{6}$ ?

Possible Answers:

135

240

5,320

2,160

Correct answer:

2,160

Explanation:

By the Binomial Theorem, the $x^{r}$ term of $(ax + b)^{n}$ is

$_{n}\textrm{C} _{r} b^{n-r}\left ( ax \right )^{r}= \frac{n!}{(n-r)!r!} a^{r} b^{n-r} x^{r}$ ,

making the coefficient of $x^{r}$

$\frac{n!}{(n-r)!r!} a^{r} b^{n-r}$ .

We can set a = 2,b=3,n=6,r=4 in this expression:

$\frac{6!}{(6-4)!4!} \cdot 2^{4} \cdot 3^{6-4}$

$=\frac{6!}{2!4!}\cdot 2^{4}\cdot 3^{2}$

$=\frac{720}{2\cdot 24}\cdot 16\cdot 9$

=2,160

Report an Error

Example Question #5 : How To Find The Exponent Of Variables

What is the coefficient of $x^{8}$ in the expansion of $(x + 3)^{10}$ ?

Possible Answers:

135

405

3,240

Correct answer:

405

Explanation:

By the Binomial Theorem, the $x^{r}$ term of $(x + b)^{n}$ is

$_{n}\textrm{C} _{r} b^{n-r} x^{r}= \frac{n!}{(n-r)!r!} b^{n-r} x^{r}$ .

Substitute b = 3, n = 10, r= 8 and this becomes

$\frac{10!}{(10-8)!8!} 3^{10-8} x^{8}$ .

The coefficient is

$\frac{10!}{(10-8)!8!} \cdot 3^{10-8} = \frac{10!}{2!8!}\cdot 3^{2} = \frac{9 \cdot 10}{2}\cdot 9 = 405$ .

Report an Error

Example Question #962 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Evaluate:

$\left [ (x^4)^4 \right ]^5$

Possible Answers:

$x^{60}$

$x^{16}$

$x^{40}$

$x^{12}$

$x^{80}$

Correct answer:

$x^{80}$

Explanation:

We need to apply the power of power rule twice:

$\left [ (x^4)^4 \right ]^5=(x^{4\times 4})^5=(x^{16})^5=x^{16\times 5}=x^{80}$

Report an Error

Example Question #1 : How To Find The Exponent Of Variables

$(x^{-4})^{a}=x^{8}$

Solve for .

Possible Answers:

Correct answer:

Explanation:

Based on the power of a product rule we have:

$(x^{-4})^{a}=x^{8}\Rightarrow x^{-4\times a}=x^8$

The bases are the same, so we can write:

$-4a=8\Rightarrow a=\frac{8}{-4}=-2$

Report an Error

Example Question #11 : Variables And Exponents

Simplify:

$(\frac{2x^5}{3y^2})^{-4}$

Possible Answers:

$\frac{81y^9}{16x^{20}}$

$\frac{81y^8}{x^{20}}$

$\frac{81y^8}{16x^{16}}$

$\frac{y^8}{16x^{20}}$

$\frac{81y^8}{16x^{20}}$

Correct answer:

$\frac{81y^8}{16x^{20}}$

Explanation:

First, recognize that raising the fraction to a negative power is the same as raising the inverted fraction to a positive power.

$(\frac{2x^5}{3y^2})^{-4}=(\frac{3y^2}{2x^5})^4$

Apply the exponent within the parentheses and simplify.

$\frac{(3y^2)^4}{(2x^5)^4}$

$\frac{3^4(y^2)^4}{2^4(x^5)^4}$

$\frac{81y^{(2\times 4)}}{16x^{(5\times 4)}}$

$\frac{81y^8}{16x^{20}}$

This fraction cannot be simplified further.

Report an Error

Example Question #1 : How To Find The Exponent Of Variables

Simplify:

$(\frac{x^2y}{2z^3})^{-2}$

Possible Answers:

$\frac{4z^8}{x^4y^2}$

$\frac{4z^6}{x^4y}$

$\frac{4z^6}{x^6y^2}$

$\frac{4z^6}{x^4y^2}$

$\frac{z^6}{x^4y^2}$

Correct answer:

$\frac{4z^6}{x^4y^2}$

Explanation:

First, recognize that raising the fraction to a negative power is the same as raising the inverted fraction to a positive power.

$(\frac{x^2y}{2z^3})^{-2}=(\frac{2z^3}{x^2y})^2$

Apply the exponent within the parentheses and simplify.

$\frac{(2z^3)^2}{(x^2y)^2}$

$\frac{2^2(z^3)^2}{(x^2)^2y^2}$

$\frac{4z^{(3\times 2)}}{x^{(2\times 2)}y^2}$

$\frac{4z^6}{x^4y^2}$

Report an Error

Example Question #971 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Simplify if $x\neq 0,-1$ and $y\neq 0$ .

$\frac{x^3y+2x^2y+xy}{xy(x+1)}$

Possible Answers:

2x+1

2x-1

x-1

x+1

Correct answer:

x+1

Explanation:

Begin by factoring the numerator and denominator. can be factored out of each term.

$\frac{x^3y+2x^2y+xy}{xy(x+1)}=\frac{xy(x^2+2x+1)}{xy(x+1)}$

can be canceled, since it appears in both the numerator and denomintor.

$\frac{x^2+2x+1}{x+1}$

Next, factor the numerator.

$\frac{(x^2+2x+1)}{x+1}=\frac{(x+1)(x+1)}{x+1}$

Simplify.

$\frac{(x+1)(x+1)}{x+1}=x+1$

Report an Error

← Previous 1 2 Next →

View Tutors

Yongmao
Certified Tutor

Nankai University, Bachelor of Science, Chemistry. Washington University in St Louis, Doctor of Philosophy, Organic Chemistry.

View Tutors

Anubhuti
Certified Tutor

KiiT University, Bachelor of Science, Electronics Technology.

View Tutors

Reuben
Certified Tutor

University of Alberta, Bachelor of Science, Mathematics.

All ISEE Upper Level Math Resources

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

Popular Subjects

Statistics Tutors in Washington DC, Algebra Tutors in San Francisco-Bay Area, Spanish Tutors in Philadelphia, GRE Tutors in Houston, Statistics Tutors in New York City, Biology Tutors in Chicago, SSAT Tutors in Seattle, English Tutors in San Diego, SAT Tutors in San Francisco-Bay Area, Reading Tutors in Seattle

Popular Courses & Classes

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

Popular Test Prep

ISEE Test Prep in Seattle, SAT Test Prep in Philadelphia, ISEE Test Prep in Dallas Fort Worth, ISEE Test Prep in Boston, ISEE Test Prep in Washington DC, LSAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Houston, LSAT Test Prep in Houston, LSAT Test Prep in Seattle, SSAT Test Prep in Houston

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 : How to find the exponent of variables

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #1 : How To Find The Exponent Of Variables

Example Question #2 : How To Find The Exponent Of Variables

Example Question #961 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #961 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #5 : How To Find The Exponent Of Variables

Example Question #962 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #1 : How To Find The Exponent Of Variables

Example Question #11 : Variables And Exponents

Example Question #1 : How To Find The Exponent Of Variables

Example Question #971 : Isee Upper Level (Grades 9 12) Mathematics Achievement

All ISEE Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: