Call Now to Set Up Tutoring:

(888) 888-0446

Pre-Algebra : Power Rule of Exponents

Study concepts, example questions & explanations for Pre-Algebra

Create An Account

All Pre-Algebra Resources

11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #74 : Polynomials

Simplify: $x^{-3}\times \frac{1}{x^3}\times x^{-3}$

Possible Answers:

$\frac{1}{x^3}$

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

x^3

x^6

$\frac{1}{x^9}$

Correct answer:

$\frac{1}{x^9}$

Explanation:

To simplify this, first convert the second term to a negative exponent.

$x^{-3}\times \frac{1}{x^3}\times x^{-3}= x^{-3}\times x^{-3}\times x^{-3}$

Since similar bases are multiplied, their powers can be added.

$x^{-3-3-3} = x^{-9} = \frac{1}{x^9}$

Report an Error

Example Question #81 : Polynomials

Solve: 3x^4+3x^2(2x^2)

Possible Answers:

9x^8

3x^4+6x^2

9x^4

9x^6

3x^4+6x^6

Correct answer:

9x^4

Explanation:

Solve by eliminating the parentheses first. When powers of the same base are multiplied, the powers can be added.

$3x^4+3x^2(2x^2) = 3x^4+ 6x^{2+2}= 3x^4+6x^4$

Combine like-terms.

3x^4+6x^4 =9x^4

Report an Error

Example Question #82 : Polynomials

Solve: $(-a)(a^4) + 2a^2\times a^4$

Possible Answers:

2a^8-a^5

2a^6-a^3

2a^6-a^4

2a^6-a^5

2a^8-a^4

Correct answer:

2a^6-a^5

Explanation:

Solve the parentheses first.

(-a)(a^4) = -a^5

Simplify the third and fourth terms.

$2a^2\times a^4 = 2a^6$

Combine or add the two terms.

2a^6-a^5

Report an Error

Example Question #83 : Polynomials

Solve: $\frac{a^4\times a^{-3}}{a^{-4}}$

Possible Answers:

$\frac{1}{a^3}$

$\frac{1}{a^4}$

a^3

a^5

Correct answer:

a^5

Explanation:

Simplify the numerator first.

$\frac{a^4\times a^{-3}}{a^{-4}} = \frac{a^{4+(-3)}}{a^{-4}} =\frac{a}{a^{-4}}$

When dividing similar bases, their powers can be subtracted.

$\frac{a}{a^{-4}} = a^{1-(-4)}=a^5$

Report an Error

Example Question #84 : Polynomials

Solve: $2b^2\cdot 3b^{-9}$

Possible Answers:

$-\frac{6 }{b^7}$

$6b^{\frac{2}{9}}$

$\large 6b^{\frac{9}{2}}$

$\frac{6}{b^7}$

$\frac{6}{b^{18}}$

Correct answer:

$\frac{6}{b^7}$

Explanation:

When similar bases are multiplied, their powers can be added together.

$2b^2\cdot 3b^{-9} = 2\cdot 3 \cdot b^{2+(-9)} = 6b^{-7}$

The next step is to eliminate the negative exponent.

Remember that a value to a negative power is one over that value to its positive power. Write the following rule:

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

Apply this rule for $6b^{-7}$ .

$6b^{-7} = 6 \cdot \frac{1}{b^7}$

Multiply the whole number with the numerator.

$6\cdot \frac{1}{b^7}= \frac{6}{b^7}$

Report an Error

Example Question #85 : Polynomials

Solve the following expression: $a^2b^4\cdot b^{-3}c^3 \cdot a^{-1}$

Possible Answers:

a^3b^3c^3

$\frac{ac^3}{b^{12}}$

$\frac{c^3}{a^2b^{12}}$

a^3b^7c^3

abc^3

Correct answer:

abc^3

Explanation:

Since every base of a certain power is all multiplied, the powers of the similar bases can be added.

Reorganize the terms.

$a^2b^4\cdot b^{-3}c^3 \cdot a^{-1} = a^2 \cdot a^{-1}\cdot b^4 \cdot b^{-3}\cdot c^3$

Simplify the bases.

$a^2 \cdot a^{-1}\cdot b^4 \cdot b^{-3}\cdot c^3 = a^{2+(-1)}b^{4+(-3)}c^3$

Add the powers to get the answer.

$a^{2+(-1)}b^{4+(-3)}c^3 = abc^3$

Report an Error

Example Question #86 : Polynomials

How do I make the following equation have a positive exponent?

7^-^5

Possible Answers:

7^5

$\frac{1}{7^5}$

$\frac{7^5}{1}$

$\frac{1}{35}$

Correct answer:

$\frac{1}{7^5}$

Explanation:

When solving a negative exponent question simply do the reciprocal of the fraction and change the sign of the exponent.

7^-^5 is really $\frac{7^-^5}{1}$ .

Recipricol means flip, so;

$\frac{1}{7^-^5}$

Then change the sign of the exponent.

$\frac{1}{7^5}$

Report an Error

Example Question #87 : Polynomials

Simplify: $\frac{21^8}{7^2}$

Possible Answers:

3^1^0

28^6

3^6

3^4

14^1^0

Correct answer:

3^6

Explanation:

When solving a division exponent question if the base is the same take it to the answer and then subtract the exponents.

In this case the bases are different so you must divide the bases then subtract the exponents.

$\frac{21^8}{7^2}$

Divide the bases: $\frac{21}{7} = 3$

Subtract the exponents: 8 - 2 = 6

The answer is 3^6

Report an Error

Example Question #88 : Polynomials

Find the solution to the equation.

(23^5)^7

Possible Answers:

23^2

23^3^5

23^1^2

23^-^2

115^7

Correct answer:

23^3^5

Explanation:

When an exponent question is in this product form we need to multiply the exponents together.

23^5^ ^* ^7 = 23^3^5

Report an Error

Example Question #89 : Polynomials

Solve the following

(a^3)^4

Possible Answers:

$a^{7}$

a^4

$a^{1}$

$a^{34}$

$a^{12}$

Correct answer:

$a^{12}$

Explanation:

When you raise a power to a power, you multiply the two powers together. So,

$(a^3)^4 = a^{3 \cdot 4} = a^{12}$

We can also look at it like this:

$(a^3)^4 = a^3 \cdot a^3 \cdot a^3 \cdot a^3$

$(a^3)^4 = a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a$

$(a^3)^4 = a^{12}$

Report an Error

View Pre-Algebra Tutors

Sharif
Certified Tutor

NCCU, Bachelors, Physics and Mathematics.

View Pre-Algebra Tutors

Alejandro
Certified Tutor

Kennesaw State University, Bachelor of Science, Computer Software Engineering.

View Pre-Algebra Tutors

Joy
Certified Tutor

Boston University, Bachelor in Arts, Conservation Biology.

All Pre-Algebra Resources

11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Statistics Tutors in Denver, Physics Tutors in San Diego, GMAT Tutors in Seattle, Math Tutors in Phoenix, Math Tutors in Miami, Statistics Tutors in Houston, Chemistry Tutors in San Diego, Physics Tutors in Philadelphia, Computer Science Tutors in San Diego, SSAT Tutors in New York City

Popular Courses & Classes

MCAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Chicago, LSAT Courses & Classes in San Diego, Spanish Courses & Classes in New York City, ISEE Courses & Classes in Seattle, ACT Courses & Classes in Los Angeles, SSAT Courses & Classes in Philadelphia, ISEE Courses & Classes in Chicago, ISEE Courses & Classes in Phoenix, ACT Courses & Classes in Dallas Fort Worth

Popular Test Prep

GRE Test Prep in Phoenix, ISEE Test Prep in Los Angeles, SSAT Test Prep in Phoenix, SSAT Test Prep in Houston, GMAT Test Prep in San Diego, ISEE Test Prep in Miami, ACT Test Prep in Philadelphia, LSAT Test Prep in Miami, SAT Test Prep in Houston, SAT Test Prep in Philadelphia

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

Pre-Algebra : Power Rule of Exponents

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #74 : Polynomials

Example Question #81 : Polynomials

Example Question #82 : Polynomials

Example Question #83 : Polynomials

Example Question #84 : Polynomials

Example Question #85 : Polynomials

Example Question #86 : Polynomials

Example Question #87 : Polynomials

Example Question #88 : Polynomials

Example Question #89 : Polynomials

All Pre-Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: