Call Now to Set Up Tutoring:

(888) 888-0446

PSAT Math : Exponents

Study concepts, example questions & explanations for PSAT Math

Create An Account

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #483 : Algebra

If $3^{4x+6}=27^{2x}$ , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

Using exponents, 27 is equal to 3³. So, the equation can be rewritten:

3^{4x + 6} = (3³)^2x

3^{4x + 6} = 3^6x

When both side of an equation have the same base, the exponents must be equal. Thus:

4x + 6 = 6x

6 = 2x

x = 3

Report an Error

Example Question #11 : How To Add Exponents

What is the value of such that 2^n=4^2*16^3*32^2 ?

Possible Answers:

240

480

Correct answer:

Explanation:

We can solve by converting all terms to a base of two. 4, 16, and 32 can all be expressed in terms of 2 to a standard exponent value.

$4=2^2\rightarrow 4^2=(2^2)^2$

$16=2^4\rightarrow 16^3=(2^4)^3$

$32=2^5\rightarrow 32^2=(2^5)^2$

We can rewrite the original equation in these terms.

2^n=(2^2)^2*(2^4)^3*(2^5)^2

Simplify exponents.

$2^n=(2^4)*(2^{12})*(2^{10})$

Finally, combine terms.

$2^n=2^{4+12+10}=2^{26}$

From this equation, we can see that n=26 .

Report an Error

Example Question #11 : Exponents

How many of the following base ten numbers have a base five representation of exactly four digits?

(A) 100

(B) 200

(D) 400

Possible Answers:

One

Four

None

Two

Three

Correct answer:

Three

Explanation:

A number in base five has powers of five as its place values; starting at the right, they are $1, 5 ^{1} = 5, 5 ^{2} = 25, 5 ^{3} = 125,5 ^{4} = 125$

The lowest base five number with four digits would be

$1000 _{\textrm{five}} = 1 \times 5^{3} = 125$ in base ten.

The lowest base five number with five digits would be

$10000 _{\textrm{five}} = 1 \times 5^{4} = 625$ in base ten.

Therefore, a number that is expressed as a four-digit number in base five must fall in the range

$125 \leq N \leq 624$

Three of the four numbers - all except 100 - fall in this range.

Report an Error

Example Question #12 : How To Add Exponents

Solve for $x$ :

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

Possible Answers:

$11$

$6$

$9$

$8$

$10$

Correct answer:

$10$

Explanation:

Combining the powers, we get $1024=2^{x}$ .

From here we can use logarithms, or simply guess and check to get $x=10$ .

Report an Error

Example Question #13 : How To Add Exponents

If $\dpi{100} \small r$ and $\dpi{100} \small s$ are positive integers, and $\dpi{100} \small 25\left ( 5^{r} \right )=5^{s-2}$ , then what is $\dpi{100} \small s$ in terms of $\dpi{100} \small r$ ?

Possible Answers:

$\dpi{100} \small r+4$

$\dpi{100} \small r$

$\dpi{100} \small r+2$

$\dpi{100} \small r+3$

$\dpi{100} \small r+1$

Correct answer:

$\dpi{100} \small r+4$

Explanation:

$\dpi{100} \small 25\left ( 5^{r} \right )$ is equal to $5^{2}\left ( 5^{r}\right )$ which is equal to $\dpi{100} \small \left ( 5^{r+2} \right )$ . If we compare this to the original equation we get $\dpi{100} \small r+2=s-2\rightarrow s=r+4$

Report an Error

Example Question #1 : How To Subtract Exponents

If m and n are integers such that m < n < 0 and m² – n² = 7, which of the following can be the value of m + n?

I. –5

II. –7

III. –9

Possible Answers:

II only

I and II only

I only

I, II and III only

II and III only

Correct answer:

II only

Explanation:

m and n are both less than zero and thus negative integers, giving us m² and n² as perfect squares. The only perfect squares with a difference of 7 is 16 – 9, therefore m = –4 and n = –3.

Report an Error

Example Question #2 : How To Subtract Exponents

$\frac{7^5+7^4}{8}=$

Possible Answers:

$\frac{7^9}{8}$

$\frac{14^4}{8}$

$\frac{7}{8}$

7^4

$\frac{7^4}{8}$

Correct answer:

7^4

Explanation:

To simplify, we can rewrite the numerator using a common exponential base.

$\frac{7^5+7^4}{8}=\frac{7(7^4)+7^4}{8}$

Now, we can factor out the numerator.

$\frac{7(7^4)+7^4}{8}=\frac{7^4(7+1)}{8}=\frac{7^4(8)}{8}$

The eights cancel to give us our final answer.

$\frac{7^4(8)}{8}=7^4$

Report an Error

Example Question #111 : Exponents

If $x\star y=x^2-y^2$ , then what is $4\star (5\star 3)$ ?

Possible Answers:

240

Correct answer:

Explanation:

$4\star (5\star 3)$

Follow the order of operations by solving the expression within the parentheses first.

$x\star y=x^2-y^2$

$5\star 3=(5)^2-(3)^2$

$5\star 3=25-9=16$

Return to solve the original expression.

$4\star(5\star3)=4\star(16)$

$x\star y=x^2-y^2$

$4\star16=(4)^2-(16)^2$

$4\star(16)=-240$

$4\star(5\star3)=-240$

Report an Error

Example Question #511 : Algebra

Solve:

$4^{8}\div2^{10}=$

Possible Answers:

-0.5

Correct answer:

Explanation:

$4^{8}=\left ( 2^{2}\right )^{8}=2^{16}$

Subtract the denominator exponent from the numerator's exponent, since they have the same base.

$\frac{2^{16}}{2^{10}}=2^{16-10}=2^{6}=64$

Report an Error

Example Question #11 : Exponents

5⁴/ 25 =

Possible Answers:

5⁴ / 5

Correct answer:

Explanation:

25 = 5 * 5 = 5². Then 5⁴ / 25 = 5⁴ / 5².

Now we can subtract the exponents because the operation is division. 5⁴ / 5²= 5^{4 – 2} = 5² = 25. The answer is therefore 25.

Report an Error

View PSAT Mathematics Tutors

Immanuel
Certified Tutor

University of Houston, Bachelor of Science, Exercise Science.

View PSAT Mathematics Tutors

Dejuan
Certified Tutor

University of Illinois at Urbana-Champaign, Bachelor of Science, Electrical Engineering.

View PSAT Mathematics Tutors

Robert
Certified Tutor

Rensselaer Polytechnic Institute, Bachelors, Electrical Engineering. Brooklyn Polytechnic, Masters, Computer Science.

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Reading Tutors in Dallas Fort Worth, SSAT Tutors in Boston, Calculus Tutors in Dallas Fort Worth, SSAT Tutors in Washington DC, GMAT Tutors in Dallas Fort Worth, SAT Tutors in Chicago, English Tutors in Chicago, GMAT Tutors in San Francisco-Bay Area, Biology Tutors in Dallas Fort Worth, English Tutors in New York City

Popular Courses & Classes

SAT Courses & Classes in Seattle, SSAT Courses & Classes in Seattle, MCAT Courses & Classes in Boston, SSAT Courses & Classes in Miami, ISEE Courses & Classes in Los Angeles, Spanish Courses & Classes in Boston, SAT Courses & Classes in Atlanta, ISEE Courses & Classes in Washington DC, MCAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in San Diego

Popular Test Prep

GRE Test Prep in Miami, SSAT Test Prep in Houston, GMAT Test Prep in Houston, MCAT Test Prep in Boston, ISEE Test Prep in Washington DC, ISEE Test Prep in Miami, GRE Test Prep in San Francisco-Bay Area, ISEE Test Prep in New York City, LSAT Test Prep in Miami, ACT Test Prep in Atlanta

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

PSAT Math : Exponents

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #483 : Algebra

Example Question #11 : How To Add Exponents

Example Question #11 : Exponents

Example Question #12 : How To Add Exponents

Example Question #13 : How To Add Exponents

Example Question #1 : How To Subtract Exponents

Example Question #2 : How To Subtract Exponents

Example Question #111 : Exponents

Example Question #511 : Algebra

Example Question #11 : Exponents

All PSAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: