Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Exponents

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #91 : Algebra Ii

Which of the following is equivalent to $3^{-2}$ ?

Possible Answers:

$\frac{1}{6}$

$\frac{1}{9}$

Correct answer:

$\frac{1}{9}$

Explanation:

By definition,

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

In our problem, b = 3 and x = 2 .

Then, we have $\frac{1}{3^{2}} = \frac{1}{9}$ .

Report an Error

Example Question #1 : Understanding Negative Exponents

Solve for :

$(x+5)^{-3} = -1$

Possible Answers:

Correct answer:

Explanation:

Raise both sides of the equation to the inverse power of to cancel the exponent on the left hand side of the equation.

$\rightarrow ((x+5)^{-3})^{-\frac{1}{3}} = (-1)^{-\frac{1}{3}}$

$\rightarrow x+5 = -1$

Subtract from both sides:

$\rightarrow (x+5) - 5 = (-1)-5$

$\rightarrow x = -6$

Report an Error

Example Question #1 : Understanding Fractional Exponents

Convert the exponent to radical notation.

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

Possible Answers:

$\small \small \sqrt[3]{x^7}$

$\small \frac{1}{x^4}$

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

$\small \small \sqrt[7]{x^3}$

Correct answer:

$\small \small \sqrt[7]{x^3}$

Explanation:

Remember that exponents in the denominator refer to the root of the term, while exponents in the numerator can be treated normally.

$x^{\frac{a}{b}}=\sqrt[b]{x^a}$

$x^{\frac{3}{7}}=\sqrt[7]{x^3}$

Report an Error

Example Question #1 : Exponents

Which of the following is equivalent to $64^{\frac{1}{2}}$ ?

Possible Answers:

$\frac{1}{32}$

Correct answer:

Explanation:

By definition, a number raised to the $\frac{1}{2}$ power is the same as the square root of that number.

Since the square root of 64 is 8, 8 is our solution.

Report an Error

Example Question #1 : Understanding Fractional Exponents

Simplify the expression:

$\small (16^{\frac{1}{2}})(256^{\frac{3}{4}})$

Possible Answers:

1024

256

Correct answer:

256

Explanation:

Remember that fraction exponents are the same as radicals.

$\small 16^{\frac{1}{2}}=\sqrt{16}=4$

$256^{\frac{3}{4}}=\sqrt[4]{256^3}=64$

A shortcut would be to express the terms as exponents and look for opportunities to cancel.

$16^{\frac{1}{2}}=(4^2)^{\frac{1}{2}}=4$

$\small 256^{\frac{3}{4}}=(4^4)^{\frac{3}{4}}=4^3=64$

Either method, we then need to multiply to two terms.

$\small (4)(64)=256$

Report an Error

Example Question #1 : Simplifying Exponents

Simplify the following expression.

$\frac{4x^3y^8z^2}{8x^6y^2z^4}$

Possible Answers:

$\frac{4y^6}{8x^3z^2}$

$\frac{4y^4}{8x^2z^2}$

$\frac{y^6}{2x^3z^2}$

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

Correct answer:

$\frac{y^6}{2x^3z^2}$

Explanation:

When dividing with exponents, the exponent in the denominator is subtracted from the exponent in the numerator. For example: $\frac{x^3}{x^6}= x^{3-6}=x^{-3}=\frac{1}{x^3}$ .

In our problem, each term can be treated in this manner. Remember that a negative exponent can be moved to the denominator.

$\frac{4x^3y^8z^2}{8x^6y^2z^4}=\frac{4}{8}x^{-3}y^6z^{-2}=\frac{4y^6}{8x^3z^2}$

Now, simplifly the numerals.

$\frac{4y^6}{8x^3z^2}=\frac{y^6}{2x^3z^2}$

Report an Error

Example Question #1 : Simplifying Exponents

Simplify the following expression.

$2^{3} \cdot 2^{6}$

Possible Answers:

$2^{18}$

$2^{9}$

$4^{18}$

$6^{6}$

$4^{9}$

Correct answer:

$2^{9}$

Explanation:

We are given: $2^{3} \cdot 2^{6}$ .

Recall that when we are multiplying exponents with the same base, we keep the base the same and add the exponents.

Thus, we have $2^{3 + 6} = 2^{9}$ .

Report an Error

Example Question #1 : Simplifying Exponents

Simplify the following expression.

$\frac{2^{9}}{2^{11}}$

Possible Answers:

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

$\frac{9}{11}$

$2^{\frac{9}{11}}$

$2^{2}$

$\frac{18}{22}$

Correct answer:

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

Explanation:

Recall that when we are dividing exponents with the same base, we keep the base the same and subtract the exponents.

Thus, we have $\frac{2^{9}}{2^{11}} = 2^{9 - 11} = 2^{-2}$ .

We also recall that for negative exponents,

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

Thus, $2^{-2} = \frac{1}{2^{2}}$ .

Report an Error

Example Question #1 : Multiplying And Dividing Exponents

Simplify the following exponent expression:

$(\frac{a^{\frac{-3}{2}}}{3^6b^{\frac{-2}{3}}})^{\frac{-1}{2}}$

Possible Answers:

$\frac{a^{\frac{3}{4}}}{b^{\frac{1}{3}}}$

$\frac{27a^{\frac{3}{4}}}{b^{\frac{1}{3}}}$

$\frac{9a^{\frac{3}{4}}}{b^{\frac{1}{3}}}$

$\frac{3a^{\frac{3}{4}}}{b^{\frac{1}{3}}}$

$\frac{18a^{\frac{3}{4}}}{b^{\frac{1}{3}}}$

Correct answer:

$\frac{27a^{\frac{3}{4}}}{b^{\frac{1}{3}}}$

Explanation:

Begin by rearranging the terms in the numerator and denominator so that the exponents are positive:

$(\frac{a^{\frac{-3}{2}}}{3^6b^{\frac{-2}{3}}})^{\frac{-1}{2}}$

$(\frac{3^6b^{\frac{-2}{3}}}{a^{\frac{-3}{2}}})^{\frac{1}{2}}$

$(\frac{3^6a^{\frac{3}{2}}}{b^{\frac{2}{3}}})^{\frac{1}{2}}$

Multiply the exponents:

$(\frac{3^3a^{\frac{3}{4}}}{b^{\frac{1}{3}}})$

Simplify:

$\frac{27a^{\frac{3}{4}}}{b^{\frac{1}{3}}}$

Report an Error

Example Question #1 : Simplifying Exponents

Simplify the expression:

$x^3 + \frac{2x^2}{x^{-1}}$

Possible Answers:

x^3+2x

x^3+2x^2

3x^3

x^3+2

$x^3+\frac{2}{x^3}$

Correct answer:

3x^3

Explanation:

First simplify the second term, and then combine the two:

$x^3 + \frac{2x^2}{x^{-1}}$

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

Report an Error

View Tutors

Sharon
Certified Tutor

Tabor College, Bachelor of Science, Mathematics Teacher Education. Tabor College, Masters in Education, Education.

View Tutors

Ramesh
Certified Tutor

california board of Accountancy, Master of Science, Accounting.

View Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

English Tutors in Atlanta, Computer Science Tutors in Denver, SSAT Tutors in Los Angeles, Reading Tutors in Denver, GMAT Tutors in Seattle, MCAT Tutors in Seattle, Physics Tutors in Philadelphia, Math Tutors in Phoenix, Statistics Tutors in San Diego, GMAT Tutors in Boston

Popular Courses & Classes

LSAT Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Seattle, LSAT Courses & Classes in Houston, LSAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Seattle, MCAT Courses & Classes in Los Angeles, SSAT Courses & Classes in Phoenix, ISEE Courses & Classes in San Diego, Spanish Courses & Classes in Houston, Spanish Courses & Classes in Miami

Popular Test Prep

SSAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in San Francisco-Bay Area, GRE Test Prep in San Francisco-Bay Area, ACT Test Prep in Denver, GRE Test Prep in Denver, SSAT Test Prep in Philadelphia, SAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Denver, ISEE Test Prep in Denver, GMAT 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

High School Math : Exponents

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #91 : Algebra Ii

Example Question #1 : Understanding Negative Exponents

Example Question #1 : Understanding Fractional Exponents

Example Question #1 : Exponents

Example Question #1 : Understanding Fractional Exponents

Example Question #1 : Simplifying Exponents

Example Question #1 : Simplifying Exponents

Example Question #1 : Simplifying Exponents

Example Question #1 : Multiplying And Dividing Exponents

Example Question #1 : Simplifying Exponents

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: