Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Mathematical Relationships and Basic Graphs

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 #150 : Multiplying And Dividing Exponents

Divide: $\frac{1}{5}\div 25^{-10}$

Possible Answers:

$\frac{5}{25^{15}}$

$5^{21}$

$25^{15}$

$\frac{5}{25^{21}}$

$5^{19}$

Correct answer:

$5^{19}$

Explanation:

In order to divide, we will first need to change the bases of both terms.

Both terms can be rewritten as base five.

$\frac{1}{5}\div 25^{-10} = 5^{-1} \div 5^{2(-10)} = \frac{5^{-1}}{5^{-20}}$

Now that bases are common, we can subtract the powers and the base will be left unchanged.

$5^{-1-(-20)} = 5^{19}$

The answer is: $5^{19}$

Report an Error

Example Question #951 : Mathematical Relationships And Basic Graphs

Evaluate: x^5*2x^2

Possible Answers:

2x^7

4x^8

4x^7

$4x^{10}$

$2x^{10}$

Correct answer:

2x^7

Explanation:

When multiplying exponents, we just add the exponents and keep the base the same.

$x^5*2x^2=2x^{5+2}=2x^7$

Report an Error

Example Question #952 : Mathematical Relationships And Basic Graphs

Evaluate: $3x^7*4x^{-2}$

Possible Answers:

$3^74^{-2}x^9$

12x^5

12x^9

$12x^{-14}$

$3^74^{-2}x^5$

Correct answer:

12x^5

Explanation:

When multiplying exponents, we just add the exponents and keep the base the same.

$3x^7*4x^{-2}=12x^{7+(-2)}=12x^5$

Report an Error

Example Question #953 : Mathematical Relationships And Basic Graphs

Simplify: $\frac{8^{2x}}{8^{2x-1}}$

Possible Answers:

$\frac{1}{8^{2x}}$

$8^{2x}$

Correct answer:

Explanation:

When dividing exponents, we just subtract the exponents and keep the base the same.

$\frac{8^{2x}}{8^{2x-1}}=8^{2x-(2x-1)}=8^{2x-2x+1}=8^{1}=8$

Report an Error

Example Question #954 : Mathematical Relationships And Basic Graphs

Simplify: $\frac{x^5y^7}{x^{5+b}y^{7-c}}$

Possible Answers:

-x^by^c

$xy^{b-c}$

$\frac{x^b}{y^c}$

$\frac{y^c}{x^b}$

x^by^c

Correct answer:

$\frac{y^c}{x^b}$

Explanation:

When dividing exponents, we just subtract the exponents and keep the base the same.

$\frac{x^5y^7}{x^{5+b}y^{7-c}}=x^{5-(5+b)y^{7-(7-c)}}=x^{-b}y^c=\frac{y^c}{x^b}$

Report an Error

Example Question #155 : Multiplying And Dividing Exponents

Solve the exponents: $4(2^{30})(8^{50})$

Possible Answers:

$4^{182}$

$64^{80}$

$32^{80}$

$8^{182}$

$2^{182}$

Correct answer:

$2^{182}$

Explanation:

To simplify, we will need to convert all bases to a common base to apply exponent properties.

2=2^1, 4=2^2, 8=2^3

We can rewrite each term using the powers of two.

$4(2^{30})(8^{50}) = (2^2)(2^{30})(2^{3(50)})= (2^2)(2^{30})(2^{150})$

Simplify the exponents. Since powers of same bases are multiplied, the powers can be added.

$2^{2+30+150} = 2^{182}$

The answer is: $2^{182}$

Report an Error

Example Question #156 : Multiplying And Dividing Exponents

Divide: $\frac{6^{-2}}{3^{-3}}$

Possible Answers:

$\frac{4}{3}$

$\frac{1}{32}$

$\frac{3}{4}$

Correct answer:

$\frac{3}{4}$

Explanation:

Simplify the negative exponents by rewriting the terms as fractions.

$\frac{6^{-2}}{3^{-3}} = \frac{\frac{1}{6^2}}{\frac{1}{3^3}}= \frac{\frac{1}{36}}{\frac{1}{27}}$

Divide the complex fractions.

$\frac{1}{36} \div \frac{1}{27} = \frac{1}{36} \times 27 =\frac{27}{36}$

Reduce this fraction.

The answer is: $\frac{3}{4}$

Report an Error

Example Question #157 : Multiplying And Dividing Exponents

Divide the exponents: $\frac{8^6}{4^8}$

Possible Answers:

$\frac{1}{4}$

$\frac{1}{2}$

Correct answer:

Explanation:

Change the base of the numerator and denominator.

They both can be rewritten as a base of two.

$\frac{8^6}{4^8} = \frac{2^{3(6)}}{2^{2(8)}} = \frac{2^{18}}{2^{16}}$

Since the bases are similar, we can subtract the exponents.

$2^{18-16} = 2^2 =4$

The answer is:

Report an Error

Example Question #155 : Simplifying Exponents

Divide: $\frac{a^3c}{a^6b^{-3}c^{-9}}$

Possible Answers:

$\frac{1}{a^3b^3c^{10}}$

$\frac{c^{10}}{a^3b^3}$

$\frac{b^3c^{10}}{a^3}$

$\frac{b^3}{a^3c^{10}}$

$\frac{b^3}{a^3c^8}$

Correct answer:

$\frac{b^3c^{10}}{a^3}$

Explanation:

For the common bases that are divided, the exponents can be subtract from numerator to denominator.

Evaluate the terms.

$\frac{a^3}{a^6} = a^{3-6} = a^{-3} = \frac{1}{a^3}$

Since there is no term on the numerator, we can assume $b^{0}=1$ .

$\frac{b^{0}}{b^{-3}} = \frac{1}{b^{-3}}= \frac{1}{\frac{1}{b^3}} = b^3$

$\frac{c^1}{c^{-9}} = c^{1-(-9)} = c^{10}$

Multiply the three terms together.

$\frac{1}{a^3}\cdot b^3 \cdot c^{10} = \frac{b^3c^{10}}{a^3}$

The answer is: $\frac{b^3c^{10}}{a^3}$

Report an Error

Example Question #156 : Simplifying Exponents

Solve: $\frac{4^{500}\times 2^{250}}{8^{125}}$

Possible Answers:

$2^{875}$

$4^{625}$

$2^{630}$

$2^{625}$

Correct answer:

$2^{875}$

Explanation:

To be able to add or subtract exponents, we should change the bases so that every base is common.

Four is two squared, and eight is two cubed. We can rewrite the numbers using base two.

$\frac{4^{500}\times 2^{250}}{8^{125}}=\frac{2^{2(500)}\times 2^{250}}{2^{3(125)}}= \frac{2^{1000}\times 2^{250}}{2^{375}}$

When exponents of the same bases are multiplied, the powers can be added. When exponents of the same base are divided, their powers can be subtracted.

$2^{1000+250-375} = 2^{875}$

The answer is: $2^{875}$

Report an Error

View Algebra 2 Tutors

Ping
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Computer Science. University of North Texas, Master of Arts, Education.

View Algebra 2 Tutors

Ridvik
Certified Tutor

University of Toronto, Bachelor of Science, Computer Engineering, General.

View Algebra 2 Tutors

Robert
Certified Tutor

University of Pittsburgh, Bachelor of Science, Physics.

All Algebra II Resources

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

Popular Subjects

LSAT Tutors in Boston, GRE Tutors in Seattle, Reading Tutors in Los Angeles, SAT Tutors in Los Angeles, Computer Science Tutors in San Francisco-Bay Area, LSAT Tutors in Phoenix, Reading Tutors in Denver, Biology Tutors in Denver, ISEE Tutors in Los Angeles, Calculus Tutors in Miami

Popular Courses & Classes

SSAT Courses & Classes in New York City, MCAT Courses & Classes in Chicago, GMAT Courses & Classes in Miami, SSAT Courses & Classes in Phoenix, GMAT Courses & Classes in San Diego, Spanish Courses & Classes in Denver, LSAT Courses & Classes in New York City, Spanish Courses & Classes in Chicago, ISEE Courses & Classes in New York City, LSAT Courses & Classes in Miami

Popular Test Prep

MCAT Test Prep in New York City, MCAT Test Prep in Miami, MCAT Test Prep in Los Angeles, ACT Test Prep in Seattle, GRE Test Prep in Denver, MCAT Test Prep in Philadelphia, ISEE Test Prep in Washington DC, GRE Test Prep in Philadelphia, GMAT Test Prep in Phoenix, GMAT Test Prep in Seattle

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 : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #150 : Multiplying And Dividing Exponents

Example Question #951 : Mathematical Relationships And Basic Graphs

Example Question #952 : Mathematical Relationships And Basic Graphs

Example Question #953 : Mathematical Relationships And Basic Graphs

Example Question #954 : Mathematical Relationships And Basic Graphs

Example Question #155 : Multiplying And Dividing Exponents

Example Question #156 : Multiplying And Dividing Exponents

Example Question #157 : Multiplying And Dividing Exponents

Example Question #155 : Simplifying Exponents

Example Question #156 : Simplifying Exponents

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: