Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Simplifying 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 #81 : Simplifying Exponents

Simplify: $4^7*4^{12}$ $\displaystyle 4^7*4^{12}$

Possible Answers:

$4^{36}$ $\displaystyle 4^{36}$

$4^{19}$ $\displaystyle 4^{19}$

$4^{84}$ $\displaystyle 4^{84}$

$4^{28}$ $\displaystyle 4^{28}$

$4^{24}$ $\displaystyle 4^{24}$

Correct answer:

$4^{19}$ $\displaystyle 4^{19}$

Explanation:

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

$4^{7}*4^{12}=4^{7+12}=4^{19}$ $\displaystyle 4^{7}*4^{12}=4^{7+12}=4^{19}$

Report an Error

Example Question #82 : Simplifying Exponents

Simplify: $5^{17}*5^{23}$ $\displaystyle 5^{17}*5^{23}$

Possible Answers:

$5^{42}$ $\displaystyle 5^{42}$

$5^{40}$ $\displaystyle 5^{40}$

$5^{391}$ $\displaystyle 5^{391}$

$5^{50}$ $\displaystyle 5^{50}$

$5^{235}$ $\displaystyle 5^{235}$

Correct answer:

$5^{40}$ $\displaystyle 5^{40}$

Explanation:

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

$5^{17}*5^{23}=5^{17+23}=5^{40}$ $\displaystyle 5^{17}*5^{23}=5^{17+23}=5^{40}$

Report an Error

Example Question #83 : Simplifying Exponents

Simplify: $\frac{6^{48}}{6^{12}}$ $\displaystyle \frac{6^{48}}{6^{12}}$

Possible Answers:

$6^{4}$ $\displaystyle 6^{4}$

$6^{24}$ $\displaystyle 6^{24}$

$6^{22}$ $\displaystyle 6^{22}$

$6{^{36}}$ $\displaystyle 6{^{36}}$

$6^{30}$ $\displaystyle 6^{30}$

Correct answer:

$6{^{36}}$ $\displaystyle 6{^{36}}$

Explanation:

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

$\frac{6^{48}}{6^{12}}=6^{48-12}=6^{36}$ $\displaystyle \frac{6^{48}}{6^{12}}=6^{48-12}=6^{36}$

Report an Error

Example Question #84 : Simplifying Exponents

Simplify: $\frac{8^{60}}{8^{-12}}$ $\displaystyle \frac{8^{60}}{8^{-12}}$

Possible Answers:

$8^{48}$ $\displaystyle 8^{48}$

$8^{-720}$ $\displaystyle 8^{-720}$

$8^{64}$ $\displaystyle 8^{64}$

$8^{80}$ $\displaystyle 8^{80}$

$8^{72}$ $\displaystyle 8^{72}$

Correct answer:

$8^{72}$ $\displaystyle 8^{72}$

Explanation:

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

$\frac{8^{60}}{8^{-12}}=8^{60-(-12)}=8^{72}$ $\displaystyle \frac{8^{60}}{8^{-12}}=8^{60-(-12)}=8^{72}$

Report an Error

Example Question #85 : Multiplying And Dividing Exponents

Simplify the following:

$\displaystyle (2a^2b^8c)(8bc^7)$

Possible Answers:

$\displaystyle 16a^2b^9c^8$

$\displaystyle 16a^2b^9c^7$

$\displaystyle 16b^9c^8$

$\displaystyle 16a^2b^8c^7$

$\displaystyle 16b^8c^7$

Correct answer:

$\displaystyle 16a^2b^9c^8$

Explanation:

Remembering the exponent rule of multiplication:

$x^m*x^n=x^{m+n}$ $\displaystyle x^m*x^n=x^{m+n}$

Therefore:

$\displaystyle (2a^2b^8c)(8bc^7)$

Becomes:

$2*8a^2b^{8+1}c^{1+7}$ $\displaystyle 2*8a^2b^{8+1}c^{1+7}$

Which gives the final answer:

$\displaystyle 16a^2b^9c^8$

Report an Error

Example Question #86 : Simplifying Exponents

Simplify:

$\frac{12a^6b^2c^3}{4ab^7c^6}$ $\displaystyle \frac{12a^6b^2c^3}{4ab^7c^6}$

Possible Answers:

$\frac{3a^6b}{c^3}$ $\displaystyle \frac{3a^6b}{c^3}$

$\displaystyle 3a^5b^5c^3$

$\frac{a^5}{3b^5c^3}$ $\displaystyle \frac{a^5}{3b^5c^3}$

$\frac{4a^5}{b^5c^3}$ $\displaystyle \frac{4a^5}{b^5c^3}$

$\frac{3a^5}{b^5c^3}$ $\displaystyle \frac{3a^5}{b^5c^3}$

Correct answer:

$\frac{3a^5}{b^5c^3}$ $\displaystyle \frac{3a^5}{b^5c^3}$

Explanation:

Using the exponent rules:

$\frac{x^m}{x^n}=x^{m-n}$ $\displaystyle \frac{x^m}{x^n}=x^{m-n}$

and:

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

Gives:

$(12/4)a^{6-1}b^{2-7}c^{3-6}=3a^5b^{-5}c^{-3}=\frac{3a^5}{b^5c^3}$ $\displaystyle (12/4)a^{6-1}b^{2-7}c^{3-6}=3a^5b^{-5}c^{-3}=\frac{3a^5}{b^5c^3}$

Report an Error

Example Question #85 : Simplifying Exponents

Simplify: $15^8*15^{12}$ $\displaystyle 15^8*15^{12}$

Possible Answers:

$15^{96}$ $\displaystyle 15^{96}$

$225^{20}$ $\displaystyle 225^{20}$

$15^{24}$ $\displaystyle 15^{24}$

$225^{96}$ $\displaystyle 225^{96}$

$15^{20}$ $\displaystyle 15^{20}$

Correct answer:

$15^{20}$ $\displaystyle 15^{20}$

Explanation:

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

$15^8*15^{12}=15^{8+12}=15^{20}$ $\displaystyle 15^8*15^{12}=15^{8+12}=15^{20}$

Report an Error

Example Question #86 : Simplifying Exponents

Simplify: $12^{-12}*12^{-9}$ $\displaystyle 12^{-12}*12^{-9}$

Possible Answers:

$12^{108}$ $\displaystyle 12^{108}$

$12^{-21}$ $\displaystyle 12^{-21}$

12^7 $\displaystyle 12^7$

$12^{-3}$ $\displaystyle 12^{-3}$

$12^{-14}$ $\displaystyle 12^{-14}$

Correct answer:

$12^{-21}$ $\displaystyle 12^{-21}$

Explanation:

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

$12^{-12}*12^{-9}=12^{-12+(-9)}=12^{-21}$ $\displaystyle 12^{-12}*12^{-9}=12^{-12+(-9)}=12^{-21}$

Report an Error

Example Question #87 : Simplifying Exponents

Simplify: $3^{-10}*3^{19}$ $\displaystyle 3^{-10}*3^{19}$

Possible Answers:

$3^{-19}$ $\displaystyle 3^{-19}$

3^9 $\displaystyle 3^9$

$3^{-29}$ $\displaystyle 3^{-29}$

3^7 $\displaystyle 3^7$

$3^{-90}$ $\displaystyle 3^{-90}$

Correct answer:

3^9 $\displaystyle 3^9$

Explanation:

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

$3^{-10}*3^{19}=3^{-10+19}=3^9$ $\displaystyle 3^{-10}*3^{19}=3^{-10+19}=3^9$

Report an Error

Example Question #88 : Simplifying Exponents

Simplify: $6^{88}\div6^{44}$ $\displaystyle 6^{88}\div6^{44}$

Possible Answers:

$6^{11}$ $\displaystyle 6^{11}$

$6^{44}$ $\displaystyle 6^{44}$

6^2 $\displaystyle 6^2$

$6^{48}$ $\displaystyle 6^{48}$

$6^{22}$ $\displaystyle 6^{22}$

Correct answer:

$6^{44}$ $\displaystyle 6^{44}$

Explanation:

When dividing exponents with the same base, we subtract the exponents while keeping the base the same.

$6^{88}\div6^{44}=6^{88-44}=6^{44}$ $\displaystyle 6^{88}\div6^{44}=6^{88-44}=6^{44}$

Report an Error

View Algebra 2 Tutors

Godswill
Certified Tutor

Rivers State University, Bachelor of Engineering, Mechanical Engineering. Texas Southern University, Master of Science, Compu...

View Algebra 2 Tutors

Keivan
Certified Tutor

University of Calgary, Doctorate (PhD), Mathematical Finance.

View Algebra 2 Tutors

Abhisek
Certified Tutor

University of Florida, Bachelor of Engineering, Computer Science.

All Algebra II Resources

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

Popular Subjects

Physics Tutors in Houston, French Tutors in Dallas Fort Worth, Calculus Tutors in Los Angeles, GMAT Tutors in Philadelphia, Computer Science Tutors in Denver, SSAT Tutors in Los Angeles, Biology Tutors in Los Angeles, Biology Tutors in Dallas Fort Worth, English Tutors in Miami, SSAT Tutors in Dallas Fort Worth

Popular Courses & Classes

MCAT Courses & Classes in Atlanta, SSAT Courses & Classes in San Diego, SAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Boston, MCAT Courses & Classes in Phoenix, GRE Courses & Classes in New York City, ISEE Courses & Classes in Houston, ACT Courses & Classes in Boston, ACT Courses & Classes in Houston

Popular Test Prep

ISEE Test Prep in Dallas Fort Worth, LSAT Test Prep in Seattle, LSAT Test Prep in Chicago, ACT Test Prep in Boston, ACT Test Prep in Houston, SAT Test Prep in Denver, MCAT Test Prep in Atlanta, GRE Test Prep in Boston, GRE Test Prep in Washington DC, SSAT 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 : Simplifying Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #81 : Simplifying Exponents

Example Question #82 : Simplifying Exponents

Example Question #83 : Simplifying Exponents

Example Question #84 : Simplifying Exponents

Example Question #85 : Multiplying And Dividing Exponents

Example Question #86 : Simplifying Exponents

Example Question #85 : Simplifying Exponents

Example Question #86 : Simplifying Exponents

Example Question #87 : Simplifying Exponents

Example Question #88 : Simplifying Exponents

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: