We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : How to divide exponents

Study concepts, example questions & explanations for ACT Math

Create An Account

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Divide Exponents

Simplify

Possible Answers:

None of the answers are correct

Correct answer:

Explanation:

When working with polynomials, dividing is the same as multiplying by the reciprocal. After multiplying, simplify. The correct answer for division is

and the correct answer for multiplication is

Report an Error

Example Question #1 : How To Divide Exponents

Simplify:

$\small \frac{x^2y^3z^4}{x^3y^4z^2}$

Possible Answers:

$\small \frac{z}{x^2y^2}$

$\small \frac{z^2}{xy}$

$\small xyz^2$

$\small \frac{yz^2}{x}$

Correct answer:

$\small \frac{z^2}{xy}$

Explanation:

To simply exponents in a fraction, subtract the exponent for each variable in the denominator from the exponent in the numerator. This will leave you with

$\small x^{-1}y^{-1}z^2$ or $\small \frac{z^2}{xy}$

Report an Error

Example Question #61 : Exponents

What is the value of m where:

n=4

$64^{\frac{n}{12}}=(m)4^{(\frac{1+m}{m+n})}$

Possible Answers:

-2

Correct answer:

Explanation:

If n=4, then 64^(4/12)=64^(1/3)=4. Then, 4=m4^(1+m)/(m+4). If 2 is substituted for m, then 4=24^(1+2)/(2+4)=24^1/2=2√4=22=4.

Report an Error

Example Question #1 : How To Divide Exponents

Simplify the following:

$\frac{x^7}{x^3}$

Possible Answers:

1/x⁴

x⁴

x^7/3

Cannot be done

Correct answer:

x⁴

Explanation:

These exponents have the same base, x, so they can be divided. To divide them, you take the exponent value in the numerator (the top exponent) and subtract the exponent value of the denominator (the bottom exponent). Here that means we take 7 – 3 so our answer is x⁴.

Report an Error

Example Question #1 : How To Divide Exponents

Simplify:

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

Possible Answers:

$8x^{6}y^{4}z$

$8x^{6}y^{5}z$

$8x^{4}y^{5}$

$8x^{4}y^{5}z$

$8x^{13}y^{3}z$

Correct answer:

$8x^{6}y^{4}z$

Explanation:

$a^{m} \cdot a^{n} = a^{m+n}$

$\frac{a^{m}}{a^{n}} = a^{m-n}$

Use rule for multiplying exponents to simplify the numerator. $\frac{8x^{8}y^{5}z}{x^{2}y}$

Use rule for dividing exponents to simplify.

$\frac{x^{8}}{x^{2}}=x^{8-2}=x^{6}$

$\frac{y^{5}}{y^{1}} = y^{5-1} = y^{4}$

$8x^{6}y^{4}z$

Report an Error

Example Question #1 : How To Divide Exponents

Simplify:

$\left (\frac{18a^3b^3}{3a^{-1}b^{-2}} \right )^2$

Possible Answers:

9a^5b^4

6a^4b^5

36a^6b^8

3a^2b^2

$36a^8b^{10}$

Correct answer:

$36a^8b^{10}$

Explanation:

Simplify:

$\left (\frac{18a^3b^3}{3a^{-1}b^{-2}} \right )^2$

Step 1: Simplify the fraction. When dividing exponents subtract the exponents on the bottom from the exponents on the top.

$\left (\frac{18a^3b^3}{3a^{-1}b^{-2}} \right )^2 =\left ( 6a^4b^5 \right )^2$

Step 2: Distribute the exponent. When raising an exponent to a power, multiply them together.

$(6a^4b^5)^2 = 36a^8b^{10}$

Report an Error

Example Question #2 : How To Divide Exponents

Simplify

$\dpi{100} \small \frac{20x^{4}y^{-3}z^{2}}{5z^{-1}y^{2}x^{2}}=$

Possible Answers:

$\dpi{100} \small {4x^{5}y^{-2}}$

$\dpi{100} \small \frac{4x^{2}z^{3}}{y^{5}}$

$\dpi{100} \small 15x^{-2}y^{-2}z^{-2}$

None

$\dpi{100} \small 15x^{2}y^{2}z^{2}$

Correct answer:

$\dpi{100} \small \frac{4x^{2}z^{3}}{y^{5}}$

Explanation:

Divide the coefficients and subtract the exponents.

Report an Error

Example Question #3 : How To Divide Exponents

Which of the following is equal to the expression Equationgre , where

xyz ≠ 0?

Possible Answers:

1/y

z/(xy)

xyz

Correct answer:

1/y

Explanation:

(xy)⁴ can be rewritten as x⁴y⁴ and z⁰ = 1 because a number to the zero power equals 1. After simplifying, you get 1/y.

Report an Error

Example Question #62 : Exponents

If $c\neq 0$ , then $\frac{(c^3)^2}{c^2c^4}=?$

Possible Answers:

c^2

c^4

Cannot be determined

Correct answer:

Explanation:

Start by simplifying the numerator and denominator separately. In the numerator, (c³)² is equal to c⁶. In the denominator, c²* c⁴ equals c⁶ as well. Dividing the numerator by the denominator, c⁶/c⁶, gives an answer of 1, because the numerator and the denominator are the equivalent.

Report an Error

Example Question #1 : How To Divide Exponents

If $a\not\equiv0$ , which of the following is equal to $\frac{(a^6*a^2)^3}{a^6}$ ?

Possible Answers:

a¹⁸

The answer cannot be determined from the above information

a⁴

a⁶

Correct answer:

a¹⁸

Explanation:

The numerator is simplified to a^8 (by adding the exponents), then cube the result. a²⁴/a⁶ can then be simplified to $a^{18}$ .

Report an Error

View ACT Math Tutors

Margaret
Certified Tutor

View ACT Math Tutors

Sarah
Certified Tutor

View ACT Math Tutors

Philip
Certified Tutor

Northern Virginia Community College, Associate in Science, Computer Science. George Mason University, Bachelor of Science, Co...

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

ACT Math Tutors in Top Cities:

Atlanta ACT Math Tutors, Austin ACT Math Tutors, Boston ACT Math Tutors, Chicago ACT Math Tutors, Dallas Fort Worth ACT Math Tutors, Denver ACT Math Tutors, Houston ACT Math Tutors, Kansas City ACT Math Tutors, Los Angeles ACT Math Tutors, Miami ACT Math Tutors, New York City ACT Math Tutors, Philadelphia ACT Math Tutors, Phoenix ACT Math Tutors, San Diego ACT Math Tutors, San Francisco-Bay Area ACT Math Tutors, Seattle ACT Math Tutors, St. Louis ACT Math Tutors, Tucson ACT Math Tutors, Washington DC ACT Math Tutors

Popular Courses & Classes

Spanish Courses & Classes in New York City, GMAT Courses & Classes in Washington DC, LSAT Courses & Classes in New York City, Spanish Courses & Classes in San Diego, SSAT Courses & Classes in San Diego, ISEE Courses & Classes in Miami, MCAT Courses & Classes in Atlanta, MCAT Courses & Classes in Seattle, ISEE Courses & Classes in Chicago, ISEE Courses & Classes in Dallas Fort Worth

Popular Test Prep

MCAT Test Prep in San Diego, GMAT Test Prep in Washington DC, ACT Test Prep in Seattle, ACT Test Prep in Phoenix, GRE Test Prep in Boston, ACT Test Prep in San Francisco-Bay Area, ACT Test Prep in New York City, SSAT Test Prep in Phoenix, GRE Test Prep in Miami, ISEE 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

ACT Math : How to divide exponents

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : How To Divide Exponents

Example Question #1 : How To Divide Exponents

Example Question #61 : Exponents

Example Question #1 : How To Divide Exponents

Example Question #1 : How To Divide Exponents

Example Question #1 : How To Divide Exponents

Example Question #2 : How To Divide Exponents

Example Question #3 : How To Divide Exponents

Example Question #62 : Exponents

Example Question #1 : How To Divide Exponents

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: