Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Math : Numbers and 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 #5 : How To Divide Exponents

Simplify:

$\frac{4x^8}{2x^0}$

Possible Answers:

x^7

2x^8

2x^7

2x^9

x^8

Correct answer:

2x^8

Explanation:

Based on the quotient rule for exponents, we know that for any non-zero number and any integers and ,

$\frac{x^a}{x^b}=x^{a-b}$ .

We also know that any non-zero number raised to the power of is .

$\frac{4x^8}{2x^0}=\frac{4}{2}\times \frac{x^8}{1}=2x^8$

Report an Error

Example Question #6 : How To Divide Exponents

Simplify:

$\frac{6x^4-6}{3x^2+3x^0}$

Possible Answers:

2(x-1)

2(x+1)

2(x^2-1)

2(x^2+1)

x^2-1

Correct answer:

2(x^2-1)

Explanation:

We know that any non-zero number raised to the power of is equal to .

$\frac{6x^4-6}{3x^2+3x^0}=\frac{6(x^4-1)}{3(x^2+x^0)}=\frac{6(x^4-1)}{3(x^2+1)}$

Now factor:

$\frac{6(x^4-1)}{3(x^2+1)}=\frac{6}{3}\frac{(x^2-1)(x^2+1)}{x^2+1}=2(x^2-1)$

Report an Error

Example Question #11 : How To Divide Exponents

Evaluate:

$\frac{4^0}{2\times 5^0-12^0}$

Possible Answers:

The expression is undefined.

$-\frac{2}{5}$

Correct answer:

Explanation:

We know that any non-zero number raised to the power of is equal to .

$\frac{4^0}{2\times 5^0-12^0}=\frac{1}{2\times 1-1}=\frac{1}{2-1}=1$

Report an Error

Example Question #41 : Exponents

Evaluate:

$\frac{y^{-2}}{y^{-5}}$

Possible Answers:

$y^{-2}$

y^3

y^2

$y^{-3}$

Correct answer:

y^3

Explanation:

Based on the quotient rule for exponents, we know that, for any non-zero number and any integers and ,

$\frac{x^a}{x^b}=x^{a-b}$ .

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

Report an Error

Example Question #12 : How To Divide Exponents

Simplify:

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

Possible Answers:

$\frac{9x^3}{y^9}$

$\frac{27x^3}{y^3}$

$\frac{27x^3}{y^6}$

$\frac{18x^3}{y^9}$

$\frac{27x^3}{y^9}$

Correct answer:

$\frac{27x^3}{y^9}$

Explanation:

When a fraction is raised to a power, the numerator and the denominator are both raised to that power:

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

The power rule says that in order to raise a power to a power, we need to multiply the exponents, i.e.

$(x^{m})^{n}=x^{m\times n}$ ,

where and are real numbers.

$(\frac{3x}{y^3})^{3}=\frac{(3x)^3}{(y^3)^3}=\frac{(3^{3}\times x^3)}{y^{3\times 3}}=\frac{27x^3}{y^9}$

Report an Error

Example Question #13 : How To Divide Exponents

Evaluate:

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

Possible Answers:

$\frac{x^4}{y^{20}}$

$\frac{x^5}{y^{20}}$

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

$\frac{x^5}{y^{9}}$

$\frac{x^5}{y^{10}}$

Correct answer:

$\frac{x^5}{y^{20}}$

Explanation:

When a fraction is raised to a power, the numerator and the denominator are both raised to that power:

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

The power rule says that in order to raise a power to a power, we need to multiply the exponents, i.e.

$(x^{m})^{n}=x^{m\times n}$ .

$(\frac{x}{y^4})^{5}=\frac{x^5}{(y^4)^5}=\frac{x^5}{y^{4\times 5}}=\frac{x^5}{y^{20}}$

Report an Error

Example Question #12 : How To Divide Exponents

Simplify:

$\frac{x^{-4}}{y^{-8}}$

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

The Negative Exponent Rule says $a^{-n}=\frac{1}{a^n}$ .

$\frac{x^{-4}}{y^{-8}}=\frac{y^8}{x^4}$

Report an Error

Example Question #13 : How To Divide Exponents

Evaluate:

$(\frac{14x^2}{7x})^0$

Assume variables are non-zero.

Possible Answers:

2x^2

Correct answer:

Explanation:

We know that any non-zero number raised to the power of is equal to .

$(\frac{14x^2}{7x})^0=1$

Report an Error

Example Question #14 : How To Divide Exponents

Evaluate:

$(\frac{22x^3}{11y})^5$

Possible Answers:

$\frac{32x^{10}}{y^5}$

$\frac{16x^{15}}{y^5}$

$\frac{32x^{15}}{y^5}$

$\frac{2x^{15}}{y^5}$

$\frac{32x^{5}}{y^5}$

Correct answer:

$\frac{32x^{15}}{y^5}$

Explanation:

When a fraction is raised to a power, the numerator and the denominator are both raised to that power. In addition, the power rule says that in order to raise a power to a power, multiply the exponents, i.e.

$(x^{m})^{n}=x^{m\times n}$ .

$(\frac{22x^3}{11y})^{5}=\frac{(22x^3)^{5}}{(11y)^5}=(\frac{22}{11})^5\times \frac{x^{3\times 5}}{y^5}=2^5\times \frac{x^{15}}{y^5}=\frac{32x^{15}}{y^5}$

Report an Error

Example Question #15 : How To Divide Exponents

What is the value of the expression $\frac{(4.2\times 10^6)}{(7.0\times 10^{-2})}$ ?

Possible Answers:

$6.0\times 10^6$

$5.0\times 10^7$

$6.0\times 10^7$

$6.0\times 10^8$

$6.0\times 10^{-6}$

Correct answer:

$6.0\times 10^7$

Explanation:

When dealing with dividing scientific notation, you can divide the like terms separately. First, divide 4.2 by 7.0. This yields 0.6. Then divide the 10s. $10^6\div 10^{-2}=10^8$ because when you divide a term with the same base, you subtract exponents. This gives you a combined answer of $0.6\times 10^8$ . Since this is not in scientific notation, move the decimal over one place to the right so that it will be in the appropriate notation. This gives you $6.0\times 10^7$ .

Report an Error

View Tutors

Gabby
Certified Tutor

University of Oregon, Bachelor in Arts, Journalism. University of Oregon, Current Grad Student, Communication, General.

View Tutors

Eva
Certified Tutor

Technicka Univerzita Liberec, Bachelor of Education, Education.

View Tutors

Jaleesa
Certified Tutor

Pomona College, Bachelors, Africana Studies.

All ISEE Upper Level Math Resources

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

Popular Subjects

French Tutors in Phoenix, SSAT Tutors in Los Angeles, Algebra Tutors in Dallas Fort Worth, English Tutors in Miami, Calculus Tutors in Dallas Fort Worth, Reading Tutors in Chicago, Computer Science Tutors in Denver, Biology Tutors in San Diego, Spanish Tutors in Los Angeles, Statistics Tutors in San Diego

Popular Courses & Classes

GRE Courses & Classes in Atlanta, MCAT Courses & Classes in Washington DC, ISEE Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Boston, GMAT Courses & Classes in Seattle, ACT Courses & Classes in New York City, MCAT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Boston, LSAT Courses & Classes in Seattle

Popular Test Prep

ISEE Test Prep in Boston, SSAT Test Prep in Denver, GRE Test Prep in Atlanta, SSAT Test Prep in Chicago, SSAT Test Prep in Dallas Fort Worth, SSAT Test Prep in San Diego, SSAT Test Prep in New York City, SAT Test Prep in Atlanta, GRE Test Prep in Houston, LSAT Test Prep in Denver

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 : Numbers and Operations

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #5 : How To Divide Exponents

Example Question #6 : How To Divide Exponents

Example Question #11 : How To Divide Exponents

Example Question #41 : Exponents

Example Question #12 : How To Divide Exponents

Example Question #13 : How To Divide Exponents

Example Question #12 : How To Divide Exponents

Example Question #13 : How To Divide Exponents

Example Question #14 : How To Divide Exponents

Example Question #15 : How To Divide 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: