We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Simple Exponents

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Simple Exponents

Simplify the following expression

$3^{8}\times3^{10}$

Possible Answers:

$3^{2}$

$3^{80}$

$3^{18}$

$3^{-2}$

Correct answer:

$3^{18}$

Explanation:

$3^{8}\times3^{10}=3^{8+10}=3^{18}$

Report an Error

Example Question #2 : Simple Exponents

Simplify the following expression

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

Possible Answers:

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

$x^{4}$

$x^{10}$

$x^{-4}$

Correct answer:

$x^{4}$

Explanation:

$\frac{x^{7}}{x^{3}}=x^{7-3}=x^{4}$

Report an Error

Example Question #201 : Understanding Exponents

Solve for x:

$3^{3x+1}=81$

Possible Answers:

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

x=3

$x=\frac{80}3{}$

$x=\frac{4}{3}$

x=1

Correct answer:

x=1

Explanation:

Solve for x:

$3^{3x+1}=81$

Step 1: Represent exponentially with a base of

$3\cdot 3\cdot 3\cdot 3=81$ , therefore 3^4=81

Step 2: Set the exponents equal to each other and solve for x

$3^{3x+1}=3^4$

3x+1 = 4

3x = 3

${\color{Red} x=1}$

Report an Error

Example Question #2 : Simple Exponents

Solve for :

$256=2^{3x+2}$

Possible Answers:

x=6

$x=84\frac{2}{3}$

x=4

x=2

x=12

Correct answer:

x=2

Explanation:

Rewrite 256 in exponential form with a base of :

$2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2=256$

2^8=256

Solve for by equating exponents:

$2^{3x+2}=2^{8}$

3x+2=8

3x=6

${\color{Red} x=2}$

Report an Error

Example Question #3333 : Algebra Ii

Solve for :

$1024=4^{2x+1}$

Possible Answers:

x=10

x=2

x=7

x=8

x=5

Correct answer:

x=2

Explanation:

Represent 1024 in exponential form using a base of :

$4\cdot 4\cdot 4\cdot 4\cdot 4=1024$

4^5=1024

Solve for by equating exponents:

$4^{2x+1}=4^5$

2x+1=5

2x=4

${\color{Red} x=2}$

Report an Error

Example Question #1 : Simple Exponents

How many perfect squares satisfy the inequality $100 \leq x \leq 1,000$ ?

Possible Answers:

Correct answer:

Explanation:

The smallest perfect square between 100 and 1,000 inclusive is 100 itself, since $10^{2} = 100$ . The largest can be found by noting that $\sqrt{1,000} \approx 31.6$ ; this makes $31^{2} = 961$ the greatest perfect square in this range.

Since the squares of the integers from 10 to 31 all fall in this range, this makes 31 - 10 + 1 = 22 perfect squares.

Report an Error

Example Question #3 : Simple Exponents

Simplify (x^2y^3)^3 .

Possible Answers:

x^1^6y^2^4^3

x^6y^9

3x^6y^9

x^5y^6

x^8y^2^7

Correct answer:

x^6y^9

Explanation:

To solve this expression, remove the outer exponent and expand the terms.

$(x^2y^3)^3=x^2\cdot x^2 \cdot x^2 \cdot y^3 \cdot y^3 \cdot y^3$

By exponential rules, add all the powers when multiplying like terms.

The answer is: x^6y^9

Report an Error

Example Question #7 : Simple Exponents

Solve for :

16=2^22^x

Possible Answers:

Correct answer:

Explanation:

The first step in solving for x is to simplify the right side:

$2^22^x=2^{2+x}$ .

Next, we can re-express the left side as an exponential with 2 as the base.

16=2^4

Now set the new left side equal to the new right side.

$2^4=2^{2+x}$

With the bases now being the same, we can simply set the exponents equal to each other.

4=2+x

x=2

Report an Error

Example Question #8 : Simple Exponents

Solve for :

$64=\frac{4^6}{4^x}$

Possible Answers:

Correct answer:

Explanation:

To solve for x, we need to simplify both sides in order to make the equation simpler to solve.

can be rewritten as 4^3 , and $\frac{4^6}{4^x}$ can be written as $4^{6-x}$ .

Setting the two sides equal to each other gives us

$4^3=4^{6-x}$

Since the bases are the same we can set the exponents equal to each other.

3=6-x

x=3

Report an Error

Example Question #4 : Simple Exponents

Evaluate:

2^5

Possible Answers:

Correct answer:

Explanation:

2^5 is expanded to 2*2*2*2*2 .

We will simply multiply the values in order to get the answer:

Report an Error

View Algebra 2 Tutors

Angela
Certified Tutor

Saint Josephs College, Bachelor in Arts, Mathematics.

View Algebra 2 Tutors

Blair
Certified Tutor

Princeton University, Bachelors, Politics. London Business School, Masters, Business Administration and Management.

View Algebra 2 Tutors

Hee
Certified Tutor

University of Missouri-Columbia, Bachelor of Science, Chemistry.

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

English Tutors in Chicago, Statistics Tutors in Phoenix, ISEE Tutors in Houston, French Tutors in Denver, GMAT Tutors in Chicago, English Tutors in Phoenix, LSAT Tutors in Philadelphia, Physics Tutors in Philadelphia, Statistics Tutors in San Francisco-Bay Area, MCAT Tutors in New York City

Popular Courses & Classes

SAT Courses & Classes in Miami, GMAT Courses & Classes in Chicago, ISEE Courses & Classes in Houston, GMAT Courses & Classes in Philadelphia, LSAT Courses & Classes in Atlanta, ACT Courses & Classes in Atlanta, GRE Courses & Classes in Philadelphia, SSAT Courses & Classes in Atlanta, MCAT Courses & Classes in Atlanta, SSAT Courses & Classes in Seattle

Popular Test Prep

GMAT Test Prep in San Diego, SSAT Test Prep in Phoenix, GMAT Test Prep in Phoenix, ISEE Test Prep in Boston, GMAT Test Prep in Chicago, GMAT Test Prep in Philadelphia, ISEE Test Prep in Chicago, SAT Test Prep in Dallas Fort Worth, MCAT Test Prep in Philadelphia, LSAT Test Prep in Houston

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

Algebra II : Simple Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #1 : Simple Exponents

Example Question #2 : Simple Exponents

Example Question #201 : Understanding Exponents

Example Question #2 : Simple Exponents

Example Question #3333 : Algebra Ii

Example Question #1 : Simple Exponents

Example Question #3 : Simple Exponents

Example Question #7 : Simple Exponents

Example Question #8 : Simple Exponents

Example Question #4 : Simple Exponents

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: