Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : Algebra

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 #2221 : Act Math

What is

$\frac{x^{-1}}{x^{-2}}$ ?

Possible Answers:

$\frac{-1}{x}$

$\frac{-1}{x^{2}}$

x^2

Correct answer:

Explanation:

Negative exponents are reciprocals. Do not change the sign to negative.

The variables with negative exponents can be written as their reciprocals.

$x^{-1} = \frac{1}{x}$

$\frac{1}{x^{-2}} = x^{2}$ ,

Multiplying these new forms together gives,

$x^{2} * \frac{1}{x}=$

$\frac{x^{2}}{x}=$

From here, simplify by factoring out a common factor from the numerator and denominator.

$\frac{x^{2}}{x}=\frac{x\cdot x}{x}=x$

Report an Error

Example Question #731 : Algebra

Simplify the following:

(xy^3)^2

Possible Answers:

$\frac{y}{x}$

$\frac{1}{x^2y^6}$

x^3y^5

x^2y^6

Correct answer:

x^2y^6

Explanation:

To solve, simply distribute the outer exponent. When you have an exponent to an exponent, you multiply their values. Thus,

$(xy^3)^2=x^{1*2}y^{3*2}=x^2y^6$

Report an Error

Example Question #2222 : Act Math

Which of the following is a value of x that satisfies

$2^{x+2}\cdot 2^{2x-3}=32$

Possible Answers:

Correct answer:

Explanation:

This question incorporates properties of exponents. The best way to solve this problem is to establish the same base for all of the terms.

$2^{x+2}\cdot 2^{2x-3}=2^{5}$

Now use the properties of exponents to simplify the left side of the equation. When exponential terms with the same base are multiplied, the exponents are added.

$2^{x+2}\cdot 2^{2x-3}=2^{(x+2)+(2x-3)}=2^{3x-1}$

Now, with the left side simplified, set that equal to $2^{5}$ .

$2^{3x-1}=2^{5}$

Since each side has one term with the same base, simply set the exponents equal to each other and solve for x.

3x-1=5

3x=6

x=2

Report an Error

Example Question #34 : Exponents

For all x, 2x² times 12x³ equals...

Possible Answers:

24x⁶

14x⁶

24x⁵

14x⁵

Correct answer:

24x⁵

Explanation:

You multiply the integers, then add the exponents on the x's, giving you 24x⁵.

Report an Error

Example Question #732 : Algebra

Multiply: 2x² * 3x

Possible Answers:

5x³

6x³

2x³

6x²

Correct answer:

6x³

Explanation:

When multiplying exponents you smiply add the exponents.

For 2x² times 3x, 2 times 3 is 6, and 2 + 1 is 3, so 2x² times 3x = 6x³

Report an Error

Example Question #3 : How To Add Exponents

What is 2³ + 2²?

Possible Answers:

Correct answer:

Explanation:

Using the rules of exponents, 2³ + 2²= 8 + 4 = 12

Report an Error

Example Question #1 : How To Add Exponents

Solve for where:

$3^{x+1}=9^{x}$

Possible Answers:

Correct answer:

Explanation:

The only value of x where the two equations equal each other is 1. All you have to do is substitute the answer choices in for x.

Report an Error

Example Question #5 : How To Add Exponents

A particle travels 9 x 10⁷ meters per second in a straight line for 12 x 10^-6 seconds. How many meters has it traveled?

Possible Answers:

1.08 x 10⁵

1.08 x 10

1.08

1.08 x 10³

Correct answer:

1.08 x 10³

Explanation:

Multiplying the two numbers yields 1080. Expressed in scientific notation 1080 is 1.08 x 10³.

Report an Error

Example Question #733 : Algebra

Simplify: hⁿ + h^–2n

Possible Answers:

$h^{-n}$

Correct answer:

Explanation:

h^–2n= 1/h²ⁿ

hⁿ + h^–2n= hⁿ + 1/h²ⁿ

Report an Error

Example Question #41 : Exponents

Simplify: 3y² + 7y² + 9y³ – y³ + y

Possible Answers:

10y⁴ + 8y⁶ + y

10y² + 10y³ + y

10y² + 8y³ + y

19y¹¹

10y² + 9y³

Correct answer:

10y² + 8y³ + y

Explanation:

Add the coefficients of similar variables (y, y², 9y³)

3y² + 7y² + 9y³ – y³ + y =

(3 + 7)y² + (9 – 1)y³ + y =

10y² + 8y³ + y

Report an Error

View ACT Math Tutors

Joshua
Certified Tutor

Cornerstone University, Bachelor in Arts, Elementary School Teaching.

View ACT Math Tutors

Elvis
Certified Tutor

Methodist University, Bachelor of Science, Mathematics and Computer Science.

View ACT Math Tutors

Chase
Certified Tutor

Western Governors University, Bachelor of Science, Mathematics.

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

SSAT Courses & Classes in Miami, LSAT Courses & Classes in Miami, LSAT Courses & Classes in Philadelphia, Spanish Courses & Classes in Washington DC, MCAT Courses & Classes in Seattle, SSAT Courses & Classes in Houston, ISEE Courses & Classes in Philadelphia, SAT Courses & Classes in Chicago, Spanish Courses & Classes in Boston, ISEE Courses & Classes in Atlanta

Popular Test Prep

MCAT Test Prep in New York City, MCAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Denver, LSAT Test Prep in Denver, SAT Test Prep in Boston, ACT Test Prep in Washington DC, MCAT Test Prep in Washington DC, SAT Test Prep in Seattle, GRE Test Prep in San Francisco-Bay Area, ACT Test Prep in Atlanta

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 : Algebra

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #2221 : Act Math

Example Question #731 : Algebra

Example Question #2222 : Act Math

Example Question #34 : Exponents

Example Question #732 : Algebra

Example Question #3 : How To Add Exponents

Example Question #1 : How To Add Exponents

Example Question #5 : How To Add Exponents

Example Question #733 : Algebra

Example Question #41 : Exponents

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: