Call Now to Set Up Tutoring:

(888) 888-0446

GED Math : Exponents

Study concepts, example questions & explanations for GED Math

Create An Account

All GED Math Resources

4 Diagnostic Tests 263 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Exponents

Order from least to greatest:

$7^{-2}, 5 ^{-2}, 2 ^{-6}$

Do not use a calculator.

Possible Answers:

$2 ^{-6}, 7^{-2}, 5 ^{-2}$

$7^{-2}, 2 ^{-6},5 ^{-2}$

$5 ^{-2} , 2 ^{-6}, 7^{-2}$

$2 ^{-6}, 5 ^{-2} , 7^{-2}$

Correct answer:

$2 ^{-6}, 7^{-2}, 5 ^{-2}$

Explanation:

For any nonzero and for any , $a^{-m} = \frac{1}{a^{m}}$ .

$7^{-2} = \frac{1}{7^{2}} = \frac{1}{7 \times 7 } = \frac{1}{49}$

$5 ^{-2} = \frac{1}{5 ^{2}} = \frac{1}{5 \times 5} = \frac{1}{25}$

$2 ^{-6} = \frac{1}{2 ^{6}} = \frac{1}{2 \times 2 \times 2 \times 2 \times 2 \times 2 } = \frac{1}{64}$

Since 25 <49 < 64 ,

we can reverse the order when taking their reciprocals:

$\frac{1}{64} < \frac{1}{49}<\frac{1}{25}$

That is, $2 ^{-6}< 7^{-2}< 5 ^{-2}$ .

Report an Error

Example Question #11 : Exponents

Order from least to greatest:

$\left (-5 \right )^{-3}, \left (-4 \right )^{-3}, \left ( -2\right ) ^{-7}$

Do not use a calculator.

Possible Answers:

$\left ( -2\right ) ^{-7} , \left (-5 \right )^{-3}, \left (-4 \right )^{-3}$

$\left ( -2\right ) ^{-7}, \left (-4 \right )^{-3} , \left (-5 \right )^{-3}$

$\left (-4 \right )^{-3} , \left (-5 \right )^{-3} , \left ( -2\right ) ^{-7}$

$\left (-5 \right )^{-3} , \left (-4 \right )^{-3} , \left ( -2\right ) ^{-7}$

Correct answer:

$\left (-4 \right )^{-3} , \left (-5 \right )^{-3} , \left ( -2\right ) ^{-7}$

Explanation:

For any nonzero and for any , $a^{-m} = \frac{1}{a^{m}}$ .

Also, any negative number raised to the power of an odd number is equal to the opposite of the same power of its absolute value.

Combine these concepts:

$\left (-5 \right )^{-3} = \frac{1 }{\left (-5 \right )^{3}} = \frac{1}{- (5^{3})} = -\frac{1}{125}$

$\left (-4 \right )^{-3} = \frac{1 }{\left (-4 \right )^{3}} = \frac{1}{- (4^{3})} = -\frac{1}{64}$

$\left ( -2\right ) ^{-7} = \frac{1}{\left ( -2\right )^{7}} = \frac{1}{- \left ( 2 ^{7}\right )} = - \frac{1}{128}$

Since 64< 125 < 128 ,

the reciprocals are in reverse order of this:

$\frac{1}{64}> \frac{1}{125 }>\frac{1}{128}$

Their opposites reverse again:

$-\frac{1}{64}<- \frac{1}{125 }<-\frac{1}{128}$

Or, equivalently,

$\left (-4 \right )^{-3} < \left (-5 \right )^{-3} < \left ( -2\right ) ^{-7}$ .

Report an Error

Example Question #151 : Complex Operations

Solve: $2^2\div 4^{3}$

Possible Answers:

$\frac{1}{2}$

$\frac{1}{16}$

$\frac{1}{12}$

$\frac{1}{32}$

Correct answer:

$\frac{1}{16}$

Explanation:

Evaluate each term first.

2^2 =4

4^3 = 64

Divide 4 with 64 and reduce.

$\frac{4}{64} = \frac{(4\times 1)}{(4\times 16)}$

The answer is: $\frac{1}{16}$

Report an Error

Example Question #481 : Ged Math

Simplify: $\frac{2^3}{6^2}$

Possible Answers:

$\frac{1}{27}$

$\frac{2}{9}$

$\frac{2}{27}$

$\frac{2}{3}$

$\frac{1}{3}$

Correct answer:

$\frac{2}{9}$

Explanation:

Do not subtract the exponents or divide the bases! We will need to compute the numerator and denominator first.

$\frac{2^3}{6^2} = \frac{(2)(2)(2)}{(6)(6)} = \frac{8}{36}$

Reduce this fraction.

The answer is: $\frac{2}{9}$

Report an Error

Example Question #482 : Numbers And Operations

Divide the following:

$m^6 \div m^2$

Possible Answers:

m^1

m^4

m^3

m^2

m^3

Correct answer:

m^4

Explanation:

To divide variables with exponents, we will use the following formula:

$x^a \div x^b = x^{a-b}$

So, we get

$m^6 \div m^2 = m^{6-2}$

$m^6 \div m^2 = m^4$

Report an Error

Example Question #483 : Numbers And Operations

Multiply the following:

$h^7 \cdot h^2$

Possible Answers:

$h^{14}$

h^3

h^5

h^9

h^7

Correct answer:

h^9

Explanation:

To multiply variables with exponents, we will use the following formula:

$x^a \cdot x^b = x^{a+b}$

So we get

$h^7 \cdot h^2 = h^{7+2}$

$h^7 \cdot h^2 = h^9$

Report an Error

Example Question #481 : Ged Math

Divide the following:

$a^{12} \div a^4$

Possible Answers:

a^8

$a^{16}$

a^2

a^4

a^3

Correct answer:

a^8

Explanation:

To divide variables with exponents, we will use the following formula:

$x^a \div x^b = x^{a-b}$

Now, let’s divide. We get

$a^{12} \div a^4 = a^{12-4}$

$a^{12} \div a^4 = a^8$

Report an Error

Example Question #482 : Ged Math

Multiply the following:

$x^9 \cdot x^2$

Possible Answers:

$x^{12}$

$x^{11}$

x^4

$x^{18}$

x^3

Correct answer:

$x^{11}$

Explanation:

To multiply variables with exponents, we will use the following formula:

$x^a \cdot x^b = x^{a+b}$

Now, we will multiply. We get

$x^9 \cdot x^2 = x^{9 + 2}$

$x^9 \cdot x^2 = x^{11}$

Report an Error

Example Question #484 : Numbers And Operations

Divide: $\frac{(-2)^3}{(-4)^{-1}}$

Possible Answers:

$\frac{1}{2}$

Correct answer:

Explanation:

Simplify the numerator.

(-2)^3=(-2)(-2)(-2) = -8

Simplify the denominator.

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

Divide the terms.

$\frac{(-2)^3}{(-4)^{-1}} = \frac{-8}{-\frac{1}{4}} = -8\div- \frac{1}{4}$

Take the reciprocal of the second term and change the sign to a multiplication.

$-8\div- \frac{1}{4} = -8\times -4 = 32$

The answer is:

Report an Error

Example Question #482 : Ged Math

Divide the following:

$n^8 \div n^2$

Possible Answers:

$n^{10}$

n^4

n^6

n^2

n^3

Correct answer:

n^6

Explanation:

To divide variables with exponents, we will use the following formula:

$x^a \div x^b = x^{a-b}$

So, we get

$n^8 \div n^2 = n^{8-2}$

$n^8 \div n^2 = n^6$

Report an Error

View Tutors

Ahlem
Certified Tutor

University of Tunis I, Bachelors, Arabic Studies and Civilisation. University of South Florida-Main Campus, Masters, French a...

View Tutors

Oluwapelumi
Certified Tutor

University of Lagos, Bachelor of Science, Pharmacy.

View Tutors

Paulina
Certified Tutor

Delta State University, Masters in Education, Elementary School Teaching.

All GED Math Resources

4 Diagnostic Tests 263 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Spanish Tutors in San Diego, ACT Tutors in Denver, Reading Tutors in Houston, Math Tutors in San Francisco-Bay Area, GMAT Tutors in Houston, Computer Science Tutors in Atlanta, MCAT Tutors in Dallas Fort Worth, MCAT Tutors in Philadelphia, SSAT Tutors in Atlanta, Math Tutors in Miami

Popular Courses & Classes

ACT Courses & Classes in Boston, ACT Courses & Classes in Phoenix, LSAT Courses & Classes in Los Angeles, ACT Courses & Classes in Atlanta, LSAT Courses & Classes in Denver, Spanish Courses & Classes in Philadelphia, SAT Courses & Classes in Phoenix, GRE Courses & Classes in Washington DC, ACT Courses & Classes in San Diego, MCAT Courses & Classes in Chicago

Popular Test Prep

ACT Test Prep in Phoenix, ACT Test Prep in Atlanta, GMAT Test Prep in Phoenix, ACT Test Prep in San Diego, SAT Test Prep in Atlanta, GRE Test Prep in Washington DC, GMAT Test Prep in New York City, SSAT Test Prep in San Diego, MCAT Test Prep in Boston, GMAT Test Prep in San Francisco-Bay Area

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

GED Math : Exponents

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #11 : Exponents

Example Question #11 : Exponents

Example Question #151 : Complex Operations

Example Question #481 : Ged Math

Example Question #482 : Numbers And Operations

Example Question #483 : Numbers And Operations

Example Question #481 : Ged Math

Example Question #482 : Ged Math

Example Question #484 : Numbers And Operations

Example Question #482 : Ged Math

All GED Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: