Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Quantitative : How to multiply 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 #101 : Numbers And Operations

Simplify: $\left (y ^{3} \right )^{4}$ $\displaystyle \left (y ^{3} \right )^{4}$

Possible Answers:

$y ^{7}$ $\displaystyle y ^{7}$

$y ^{12}$ $\displaystyle y ^{12}$

The correct answer is not among the other choices.

$y ^{64}$ $\displaystyle y ^{64}$

$y ^{81}$ $\displaystyle y ^{81}$

Correct answer:

$y ^{12}$ $\displaystyle y ^{12}$

Explanation:

Apply the power of a power property:

$\left (y ^{3} \right )^{4} = y ^{3 \cdot 4} = y^{12}$ $\displaystyle \left (y ^{3} \right )^{4} = y ^{3 \cdot 4} = y^{12}$

Report an Error

Example Question #2 : Exponential Operations

Simplify the expression: $\left (5 a^{3}y ^{4} \right )^{2}$ $\displaystyle \left (5 a^{3}y ^{4} \right )^{2}$

Possible Answers:

$25a^{6} y^{8}$ $\displaystyle 25a^{6} y^{8}$

$25a^{9} y^{16}$ $\displaystyle 25a^{9} y^{16}$

$10a^{6} y^{8}$ $\displaystyle 10a^{6} y^{8}$

$10a^{9} y^{16}$ $\displaystyle 10a^{9} y^{16}$

$10a^{5} y^{6}$ $\displaystyle 10a^{5} y^{6}$

Correct answer:

$25a^{6} y^{8}$ $\displaystyle 25a^{6} y^{8}$

Explanation:

Apply the power of a product rule, then apply the power of a power rule:

$\left (5 a^{3}y ^{4} \right )^{2}$ $\displaystyle \left (5 a^{3}y ^{4} \right )^{2}$

$= 5^{2} \cdot \left (a^{3}\right )^{2} \cdot \left ( y ^{4} \right )^{2}$ $\displaystyle = 5^{2} \cdot \left (a^{3}\right )^{2} \cdot \left ( y ^{4} \right )^{2}$

$= 25 \cdot a^{ 3 \cdot 2 } \cdot y ^{ 4 \cdot 2 }$ $\displaystyle = 25 \cdot a^{ 3 \cdot 2 } \cdot y ^{ 4 \cdot 2 }$

$= 25 a^{ 6} y ^{ 8 }$ $\displaystyle = 25 a^{ 6} y ^{ 8 }$

Report an Error

Example Question #1 : How To Multiply Exponents

Which of the following expressions is equal to $1,234^{0}$ $\displaystyle 1,234^{0}$ ?

Possible Answers:

$\displaystyle 1$

The expression is undefined.

1,234 $\displaystyle 1,234$

$\displaystyle 0$

$\frac{1}{1,234 }$ $\displaystyle \frac{1}{1,234 }$

Correct answer:

$\displaystyle 1$

Explanation:

Any nonzero number raised to the power of 0 is equal to 1.

Report an Error

Example Question #1 : How To Multiply Exponents

Which quantity is greater?

(a) $(-5) ^{3}$ $\displaystyle (-5) ^{3}$

(b) $(-5) ^{-3}$ $\displaystyle (-5) ^{-3}$

Possible Answers:

(b) is greater.

(a) is greater.

It is impossible to tell from the information given.

(a) and (b) are equal.

Correct answer:

(b) is greater.

Explanation:

(a) $(-5) ^{3} = (-5) \cdot (-5) \cdot (-5) = 25 \cdot (-5) = -125$ $\displaystyle (-5) ^{3} = (-5) \cdot (-5) \cdot (-5) = 25 \cdot (-5) = -125$

(b) $(-5) ^{-3} = \frac{1}{(-5) ^{3}} = \frac{1}{-125} =- \frac{1}{125}$ $\displaystyle (-5) ^{-3} = \frac{1}{(-5) ^{3}} = \frac{1}{-125} =- \frac{1}{125}$

(b) is the greater quantity.

Report an Error

Example Question #104 : Numbers And Operations

$\displaystyle x$ is positive.

Which is the greater quantity?

(a) $100 ^{2x}$ $\displaystyle 100 ^{2x}$

(b) $1,000 ^{x}$ $\displaystyle 1,000 ^{x}$

Possible Answers:

It is impossible to tell from the information given

(a) and (b) are equal

(a) is greater

(b) is greater

Correct answer:

(a) is greater

Explanation:

Use the power of a power property:

(a) $100 ^{2x} = \left (10^{2} \right ) ^{2x} = 10^{2\cdot 2x }= 10^{4x }$ $\displaystyle 100 ^{2x} = \left (10^{2} \right ) ^{2x} = 10^{2\cdot 2x }= 10^{4x }$

(b) $1,000 ^{x} =\left ( 1 0 ^{3} \right ) ^{x} = 1 0 ^{3x}$ $\displaystyle 1,000 ^{x} =\left ( 1 0 ^{3} \right ) ^{x} = 1 0 ^{3x}$

Since x > 0 $\displaystyle x > 0$ , 4x > 3x $\displaystyle 4x > 3x$ . Subsequently,

$100 ^{2x} = 10^{4x } > 10^{3x } = 1,000^{x }$ $\displaystyle 100 ^{2x} = 10^{4x } > 10^{3x } = 1,000^{x }$ ,

making (a) greater

Report an Error

Example Question #5 : How To Multiply Exponents

Which is the greater quantity?

(a) $2 ^{100}$ $\displaystyle 2 ^{100}$

(b) $4^{50}$ $\displaystyle 4^{50}$

Possible Answers:

(a) is greater

(b) is greater

(a) and (b) are equal

It is impossible to tell from the information given

Correct answer:

(a) and (b) are equal

Explanation:

$4^{50} = \left ( 2 ^{2} \right )^{50} = 2 ^{ 2\; \cdot \;50 } = 2 ^{ 100 }$ $\displaystyle 4^{50} = \left ( 2 ^{2} \right )^{50} = 2 ^{ 2\; \cdot \;50 } = 2 ^{ 100 }$

The two quantities are equal.

Report an Error

Example Question #1 : How To Multiply Exponents

Two quantities are given - one in Column A and the other in Column B. Compare the quantities in the two columns.

Assume, in both columns, that $x\neq0$ $\displaystyle x\neq0$ .

Column A Column B

$x^{4}\cdot x^2$ $\displaystyle x^{4}\cdot x^2$ $\frac{x^{11}}{x^{2}}$ $\displaystyle \frac{x^{11}}{x^{2}}$

Possible Answers:

The quantity in Column B is greater.

The quantities in both columns are equal.

The quantity in Column A is greater.

There is no way to determine the relationship between the columns.

Correct answer:

There is no way to determine the relationship between the columns.

Explanation:

Column A gives simplifies to give us $\ x^{6}$ $\displaystyle \ x^{6}$ , and Column B simplifies to give us $x^{9}$ $\displaystyle x^{9}$ . At first glance, Column B is greater, as it would be for all answers greater than 1. However, if x=1 $\displaystyle x=1$ , the two columns are equal. Furthermore, if $\displaystyle x$ is negative, or a fraction, Column A is greater. Thus, since we could arrive at all three answers by using different numbers, we cannot determine the answer conclusively.

Report an Error

Example Question #8 : How To Multiply Exponents

Which of the following expressions is equivalent to

$\left (\sqrt{1,001}-\sqrt{999} \right ) \left ( \sqrt{1,001}+\sqrt{999} \right )$ $\displaystyle \left (\sqrt{1,001}-\sqrt{999} \right ) \left ( \sqrt{1,001}+\sqrt{999} \right )$ ?

Possible Answers:

$\sqrt{2}$ $\displaystyle \sqrt{2}$

$20\sqrt{5}$ $\displaystyle 20\sqrt{5}$

$\displaystyle 2$

2,000 $\displaystyle 2,000$

$2,000 - 3 \sqrt{111,111}$ $\displaystyle 2,000 - 3 \sqrt{111,111}$

Correct answer:

$\displaystyle 2$

Explanation:

Use the difference of squares pattern as follows:

$\left (\sqrt{1,001}-\sqrt{999} \right ) \left ( \sqrt{1,001}+\sqrt{999} \right )$ $\displaystyle \left (\sqrt{1,001}-\sqrt{999} \right ) \left ( \sqrt{1,001}+\sqrt{999} \right )$

$= \left (\sqrt{1,001} \right ) ^{2} - \left (\ \sqrt{999} \right ) ^{2}$ $\displaystyle = \left (\sqrt{1,001} \right ) ^{2} - \left (\ \sqrt{999} \right ) ^{2}$

$\displaystyle =1,001 - 999 = 2$

Report an Error

Example Question #1 : Exponents

Column A Column B

$\left ( \frac{5x^2}{25y^4} \right )^{0}$ $\displaystyle \left ( \frac{5x^2}{25y^4} \right )^{0}$ $\displaystyle 0$

Possible Answers:

The quantity in Column B is greater.

The quantity in Column A is greater.

The quantities in both columns are equal.

No relationship between the columns can be determined.

Correct answer:

The quantity in Column A is greater.

Explanation:

Anything raised to zero is equal to 1. Therefore, Column A has to be greater because 1 is greater than 0.

Report an Error

Example Question #2 : Exponents

44,000,000 can be written in scientific notation as $a \times 10 ^{N}$ $\displaystyle a \times 10 ^{N}$ for some a, N $\displaystyle a, N$ .

Which is the greater quantity?

(A) $\displaystyle N$

(B) 8

Possible Answers:

(A) is greater

It is impossible to determine which is greater from the information given

(A) and (B) are equal

(B) is greater

Correct answer:

(B) is greater

Explanation:

To write 44,000,000 in scientifc notation, write the implied decimal point after the final "0", then move it left until it is after the first nonzero digit (the first "4").

$44 000 000. \Rightarrow 4.4 000 000$ $\displaystyle 44 000 000. \Rightarrow 4.4 000 000$

This requires a displacement of seven places, so

$44,000,000 = 4.4 \times 10^{7}$ $\displaystyle 44,000,000 = 4.4 \times 10^{7}$

$\displaystyle N = 7 < 8$ , and (B) is greater.

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

Cheryl
Certified Tutor

Palm Beach Atlantic University-West Palm Beach, Bachelor of Science, Business Administration and Management. Southern New Ham...

View Tutors

Ericka
Certified Tutor

Southern Nazarene University, Bachelors, Network Engineering and Management . Oklahoma State University-Main Campus, Master o...

All ISEE Upper Level Quantitative Resources

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

Popular Subjects

LSAT Tutors in Miami, Statistics Tutors in New York City, Math Tutors in Denver, ISEE Tutors in San Diego, GRE Tutors in Denver, Statistics Tutors in Washington DC, Biology Tutors in Boston, MCAT Tutors in San Diego, Physics Tutors in Miami, Biology Tutors in Atlanta

Popular Courses & Classes

GRE Courses & Classes in Miami, Spanish Courses & Classes in Miami, GMAT Courses & Classes in Los Angeles, ACT Courses & Classes in Chicago, ACT Courses & Classes in Seattle, ISEE Courses & Classes in New York City, SAT Courses & Classes in Seattle, LSAT Courses & Classes in Seattle, MCAT Courses & Classes in Phoenix, MCAT Courses & Classes in New York City

Popular Test Prep

ACT Test Prep in Seattle, LSAT Test Prep in Atlanta, ACT Test Prep in Chicago, GMAT Test Prep in Los Angeles, GRE Test Prep in Houston, LSAT Test Prep in Boston, LSAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Philadelphia, ISEE Test Prep in Washington DC, LSAT Test Prep in Phoenix

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 multiply exponents

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

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #101 : Numbers And Operations

Example Question #2 : Exponential Operations

Example Question #1 : How To Multiply Exponents

Example Question #1 : How To Multiply Exponents

Example Question #104 : Numbers And Operations

Example Question #5 : How To Multiply Exponents

Example Question #1 : How To Multiply Exponents

Example Question #8 : How To Multiply Exponents

Example Question #1 : Exponents

Example Question #2 : 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: