Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Quantitative : How to divide exponents

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

Create An Account

All ISEE Upper Level Quantitative Resources

8 Diagnostic Tests 234 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Divide Exponents

$\frac{ \left ( 30 -2 \cdot 15\right )^{0}}{\left ( 30 -15\right )^{0}}$

Possible Answers:

The expression is undefined.

Correct answer:

The expression is undefined.

Explanation:

$\frac{ \left ( 30 -2 \cdot 15\right )^{0}}{\left ( 30 -15\right )^{0}} = \frac{ \left ( 30 -30\right )^{0}}{15^{0}}=\frac{ 0^{0}}{15^{0}}$

The numerator is undefined, since 0 raised to the power of 0 is an undefined quantity. Therefore, the entire expression is undefined.

Report an Error

Example Question #2 : How To Divide Exponents

Column A Column B

$\left(\frac{1}{16}\right)^\frac{1}{2}$ $\left(\frac{1}{16}\right)^{-\frac{1}{2}}$

Possible Answers:

There is not enough information to determine the relationship between the quantities.

The quantity in Column A is greater.

The quantity in Column B is greater.

The quantities are equal.

Correct answer:

The quantity in Column B is greater.

Explanation:

Let's simplify both quantities first before we compare them. $\left(\frac{1}{16}\right)^\frac{1}{2}$ becomes $\sqrt{\frac{1}{16}}$ because the fractional exponent indicates a square root. We can simplify that by knowing that we can take the square roots of both the numerator and denominator, as shown by: $\frac{\sqrt{1}}{\sqrt{16}}$ . We can simplify further by taking the square roots (they're perfect squares) and get $\frac{1}{4}$ . Then, let's simplify Column B. To get rid of the negative exponent, we put the numerical expression on the denominator. There's still the fractional exponent at play, so we'll have a square root as well. It looks like this now: $\frac{1}{\sqrt{\frac{1}{16}}}$ . We already simplified $\sqrt{\frac{1}{16}}$ , so we can just plug in our answer, $\frac{1}{4}$ , into the denominator. Since we don't want a fraction in the denominator, we can multiply by the reciprocal of $\frac{1}{4}$ , which is 4 to get 1(4) , which is just 4. Therefore, Column B is greater.

Report an Error

Example Question #3 : How To Divide Exponents

Give the reciprocal of $1.6 \times 10 ^{-7}$ in scientific notation.

Possible Answers:

$6.25 \times 10^{6 }$

$6.25 \times 10^{-7 }$

$6.25 \times 10^{8 }$

$6.25 \times 10^{7 }$

$6.25 \times 10^{-6 }$

Correct answer:

$6.25 \times 10^{6 }$

Explanation:

The reciprocal of $1.6 \times 10 ^{-7}$ is the quotient of 1 and the number;

$\frac{1}{ 1.6 \times 10 ^{-7} }$

$= \frac{1 \times 10^{0}}{ 1.6 \times 10 ^{-7} }$

$= \frac{1 }{ 1.6 } \times \frac{ 10^{0}}{ 10 ^{-7} }$

$=0.625 \times 10^{0- (-7) }$

$=0.625 \times 10^{7 }$

This is not in scientific notation, so adjust.

$6.25 \times 10^{-1 } \times 10^{7 }$

$= 6.25 \times 10^{-1+7 }$

$= 6.25 \times 10^{6 }$

Report an Error

Example Question #1 : How To Divide Exponents

Give the reciprocal of $3.2 \times 10 ^{9}$ in scientific notation.

Possible Answers:

$-3.2 \times 10 ^{-10}$

$3.125 \times 10 ^{-10}$

$3.125 \times 10 ^{-9}$

$-3.2 \times 10 ^{-9}$

$-3.125 \times 10 ^{9}$

Correct answer:

$3.125 \times 10 ^{-10}$

Explanation:

The reciprocal of $3.2 \times 10 ^{9}$ is the quotient of 1 and the number, or

$\frac{1}{ 3.2 \times 10 ^{9} }$

$= \frac{1 \times 10^{0}}{ 3.2 \times 10 ^{9}}$

$= \frac{1 }{ 3.2 } \times \frac{ 10^{0}}{ 10 ^{9} }$

$=0.3125 \times 10 ^{-9}$

This is not in scientific notation, so adjust:

$3.125 \times 10 ^{-1}\times 10 ^{-9}$

$=3.125 \times 10 ^{-1+ (-9)}$

$=3.125 \times 10 ^{-10}$

Report an Error

Example Question #1 : How To Divide Exponents

x> 1

Column A Column B

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

Possible Answers:

The quantity in Column B is greater.

The quantities in both columns are equal.

The relationship between the columns cannot be determined.

The quantity in Column A is greater.

Correct answer:

The quantity in Column A is greater.

Explanation:

You can simplify Column A first. When you're dividing with exponents and bases are the same, subtract the exponents. Therefore, it simplifies to x. We know that x is positive since it is greater than 1. X is greater than $\sqrt{x}$ . Try plugging in a number to test. 25 is greater than $\sqrt{25}$ , which is 5. Even 1.1 is greater than $\sqrt{1.1}$ . Therefore, Column A is greater.

Report an Error

View Tutors

Jeromy
Certified Tutor

Washington State University, Bachelor of Science, Psychology. University of Washington-Seattle Campus, Master of Arts Teachin...

View Tutors

Robert
Certified Tutor

University of North Carolina at Chapel Hill, Bachelor in Arts, English. North Carolina Central University, Master of Arts, En...

View Tutors

Caroline
Certified Tutor

University of Florida, Bachelor of Science, Psychology.

All ISEE Upper Level Quantitative Resources

8 Diagnostic Tests 234 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Chemistry Tutors in Atlanta, SAT Tutors in Boston, GRE Tutors in Miami, Reading Tutors in Denver, Calculus Tutors in Chicago, Reading Tutors in Atlanta, Math Tutors in Washington DC, ISEE Tutors in Atlanta, English Tutors in Seattle, Math Tutors in Miami

Popular Courses & Classes

Spanish Courses & Classes in Miami, ISEE Courses & Classes in Philadelphia, ISEE Courses & Classes in Los Angeles, ACT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Phoenix, SAT Courses & Classes in Houston, Spanish Courses & Classes in San Diego, MCAT Courses & Classes in Miami, GRE Courses & Classes in Denver, GMAT Courses & Classes in Boston

Popular Test Prep

SSAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Phoenix, ISEE Test Prep in San Diego, MCAT Test Prep in Chicago, LSAT Test Prep in Boston, ACT Test Prep in Dallas Fort Worth, SSAT Test Prep in Philadelphia, GRE Test Prep in Washington DC, GRE Test Prep in Houston, GMAT Test Prep in San Diego

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 Quantitative : How to divide exponents

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

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #1 : How To Divide Exponents

Example Question #2 : How To Divide Exponents

Example Question #3 : How To Divide Exponents

Example Question #1 : How To Divide Exponents

Example Question #1 : How To Divide Exponents

All ISEE Upper Level Quantitative Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: