Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : How to find a ratio of 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 : Exponential Ratios

If $x^{2}=25$ and $y^{4}=81$ , then which of the following CANNOT be the value of x + y ?

Possible Answers:

Correct answer:

Explanation:

Even roots of numbers can either be positive or negative. Thus, x = +/- 5 and y = +/- 3. The possible values from x + y can therefore be:

(-5) + (-3) = -8

(-5) + 3 = -2

5 + (-3) = 2

5 + 3 = 8

Report an Error

Example Question #2 : Exponential Ratios

If $\frac{n^{y}}{n^{x}}=n^{6}$ for all $\dpi{100} \small n$ not equal to 0, which of the following must be true?

Possible Answers:

$\dpi{100} \small y-x = 6$

$\dpi{100} \small y+x = 6$

$\dpi{100} \small yx = 6$

$\dpi{100} \small \frac{x}{y} = 6$

$\dpi{100} \small \frac{y}{x} = 6$

Correct answer:

$\dpi{100} \small y-x = 6$

Explanation:

Remember that $\dpi{100} \small \frac{n^{y}}{n^{x}}=n^{y-x}$

Since the problem states that $\frac{n^{y}}{n^{x}}=n^{6}$ , you can assume that $\dpi{100} \small n^{y-x}=n^{6}$

This shows that $\dpi{100} \small y-x = 6$ .

Report an Error

Example Question #3 : Exponential Ratios

If and are positive integers and , then what is the value of $\frac{m}{n}$ ?

Possible Answers:

$\frac{1}{16}$

$\frac{5}{3}$

$\frac{1}{3}$

Correct answer:

Explanation:

4³= 64

Alternatively written, this is 4(4)(4) = 64 or 4³= 64^1.

Thus, m = 3 and n = 1.

m/n = 3/1 = 3.

Report an Error

Example Question #4 : Exponential Ratios

Write the following logarithm in expanded form:

$\log x^{2}y$

Possible Answers:

$2\log x+\log y$

$\log x+\log y$

$2\log x-\log y$

$\log x^{2}+\log y$

$2\left ( \log xy \right )$

Correct answer:

$2\log x+\log y$

Explanation:

$\log x^{2}y=\log x^{2}+\log y=2\log x+\log y$

Report an Error

Example Question #5 : Exponential Ratios

If and are both rational numbers and $4^{m} = 8^{n}$ , what is $\frac{m}{n}$ ?

Possible Answers:

$\frac{2}{1}$

$\frac{5}{3}$

$\frac{4}{1}$

$\frac{3}{2}$

Correct answer:

$\frac{3}{2}$

Explanation:

This question is asking you for the ratio of m to n. To figure it out, the easiest way is to figure out when 4 to an exponent equals 8 to an exponent. The easiest way to do that is to list the first few results of 4 to an exponent and 8 to an exponent and check to see if any match up, before resorting to more drastic means of finding a formula.

$4^{1} = 4, 4^{2} = 16, 4^{3} = 64, 4^{4} = 256, 4^{5} = 1024$

$8^{1}=8, 8^{2} = 64, 8^{3} = 512, 8^{4} = 4096, 8^{5} = 32768$

And, would you look at that. $4^{3}= 8^{2}$ . Therefore, $\frac{m}{n} = \frac{3}{2}$ .

Report an Error

View ACT Math Tutors

Shane
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Computer Engineering, General.

View ACT Math Tutors

Yucheng
Certified Tutor

The University of Texas at Austin, Bachelor of Science, Mechanical Engineering.

View ACT Math Tutors

Jonathan
Certified Tutor

University of Illinois at Chicago, Bachelor in Arts, Criminal Justice. Syracuse University, Masters in Business Administratio...

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

SAT Courses & Classes in Chicago, ISEE Courses & Classes in Chicago, SSAT Courses & Classes in Washington DC, Spanish Courses & Classes in Boston, SSAT Courses & Classes in Phoenix, GMAT Courses & Classes in Chicago, SAT Courses & Classes in Denver, MCAT Courses & Classes in Los Angeles, LSAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Miami

Popular Test Prep

SSAT Test Prep in Chicago, MCAT Test Prep in Phoenix, LSAT Test Prep in Chicago, GMAT Test Prep in Chicago, ISEE Test Prep in Dallas Fort Worth, MCAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Los Angeles, ISEE Test Prep in Phoenix, ISEE Test Prep in Miami, 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

ACT Math : How to find a ratio of exponents

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : Exponential Ratios

Example Question #2 : Exponential Ratios

Example Question #3 : Exponential Ratios

Example Question #4 : Exponential Ratios

Example Question #5 : Exponential Ratios

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: