Call Now to Set Up Tutoring:

(888) 888-0446

PSAT Math : How to add 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 #71 : Exponents

If a² = 35 and b² = 52 then a⁴ + b⁶ = ?

Possible Answers:

522

140,608

3929

141,833

150,000

Correct answer:

141,833

Explanation:

a⁴= a² * a² and b⁶= b² * b²* b²

Therefore a⁴ + b⁶ = 35 * 35 + 52 * 52 * 52 = 1,225 + 140,608 = 141,833

Report an Error

Example Question #93 : Exponents

If $9^{(x + 5)}+3^{2(x+5)}=162$ , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

Since we have two ’s in $9^{(x + 5)} + 3^{2(x + 5)}$ we will need to combine the two terms.

For $3^{2(x + 5) }$ this can be rewritten as

$(3^2)^{ (x + 5)} = 9^ {(x + 5)}$

So we have $9^{ (x + 5) }+ 9^{ (x + 5)} = 162$ .

Or $2 (9^{ (x + 5)}) = 162$

Divide this by : $9^{ (x + 5)} = 81 = 9^ 2$

Thus x +5 = 2 or x = -3

*Hint: If you are really unsure, you could have plugged in the numbers and found that the first choice worked in the equation.

Report an Error

Example Question #72 : Exponents

Solve for x.

2³+ 2^x+1= 72

Possible Answers:

Correct answer:

Explanation:

The answer is 5.

8 + 2^x+1= 72

2^x+1= 64

2^x+1= 2⁶

x + 1 = 6

x = 5

Report an Error

Example Question #73 : Exponents

Which of the following is eqivalent to 5^b – 5^(b–1) – 5^(b–1)– 5^(b–1)– 5^(b–1)– 5^(b–1), where b is a constant?

Possible Answers:

5^b–1

1/5

Correct answer:

Explanation:

We want to simplify 5^b – 5^(b–1)– 5^(b–1)– 5^(b–1)– 5^(b–1)– 5^(b–1).

Notice that we can collect the –5⁽^b–1) terms, because they are like terms. There are 5 of them, so that means we can write –5^(b–1)– 5^(b–1)– 5^(b–1)– 5^(b–1)– 5^(b–1)as (–5^(b–1))5.

To summarize thus far:

5^b – 5^(b–1)– 5^(b–1)– 5^(b–1)– 5^(b–1)– 5^(b–1)= 5^b +(–5^(b–1))5

It's important to interpret –5^(b–1)as (–1)5^(b–1) because the –1 is not raised to the (b – 1) power along with the five. This means we can rewrite the expression as follows:

5^b +(–5^(b–1))5 = 5^b + (–1)(5^(b–1))(5) = 5^b – (5^(b–1))(5)

Notice that 5⁽^b–1) and 5 both have a base of 5. This means we can apply the property of exponents which states that, in general, a^ba^c = a^b+c. We can rewrite 5 as 5¹ and then apply this rule.

5^b – (5^(b–1))(5) = 5^b – (5^(b–1))(5¹) = 5^b – 5^(b–1+1)

Now, we will simplify the exponent b – 1 + 1 and write it as simply b.

5^b – 5^(b–1+1)= 5^b – 5^b = 0

The answer is 0.

Report an Error

Example Question #74 : Exponents

If $x^2=11$ , then what does $x^4$ equal?

Possible Answers:

121

110

144

Correct answer:

121

Explanation:

$x^4=(x^2)(x^2)=11\cdot 11=121$

Report an Error

Example Question #3 : Exponents

Simplify. All exponents must be positive.

$\left ( x^{-2}y^{3} \right )\left ( x^{5}y^{-4} \right )$

Possible Answers:

$\left ( x^{-2}+x^{5} \right )\left ( y^{3}+y^{-4} \right )$

$x^{3}y^{-2}$

$x^{2}y^{7}$

$x^{7}y^{7}$

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

Correct answer:

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

Explanation:

Step 1: $\left ( x^{-2}x^{5} \right )= x^{3}$

Step 2: $\left ( y^{3}y^{-4} \right )= y^{-1}= \frac{1}{y}$

Step 3: (Correct Answer): $\frac{x^{3}}{y}$

Report an Error

Example Question #1 : Exponents

Simplify. All exponents must be positive.

$\frac{x^{-3}y^{5}}{x^{2}y^{-1}}$

Possible Answers:

$\frac{y^{6}}{x^{5}}$

$\frac{\left ( xy \right )^{2}}{\left ( xy \right )}$

$\frac{1}{x^{5}y^{-6}}$

$x^{-5}y^{6}$

$x^{-1}y^{4}$

Correct answer:

$\frac{y^{6}}{x^{5}}$

Explanation:

Step 1: $\frac{y^{5}}{\left ( x^{3}x^{2} \right )\left \right )y^{-1}}$

Step 2: $\frac{\left ( y^{5}y^{1} \right )}{x^{3}x^{2}}$

Step 3: $\frac{y^{6}}{x^{5}}$

Report an Error

Example Question #75 : Exponents

$\frac{\left ( -11 \right )^{-8}}{\left ( -11\right )^{12}}$

Answer must be with positive exponents only.

Possible Answers:

$\left ( -11 \right )^{4}$

$\left ( 1 \right )^{-20}$

$\frac{1}{\left ( -11 \right )^{20}}$

$\left ( -11 \right )^{-20}$

$\frac{1}{\left ( -11 \right )^{4}}$

Correct answer:

$\frac{1}{\left ( -11 \right )^{20}}$

Explanation:

Step 1: $\frac{1}{\left ( -11 \right )^{12}\left ( -11 \right )^{8}}$

Step 2: The above is equal to $\frac{1}{\left ( -11 \right )^{20}}$

Report an Error

Example Question #1 : Exponents

Evaluate:

$-\left ( -3 \right )^{0}-\left ( -3^{0} \right )$

Possible Answers:

Correct answer:

Explanation:

$-\left ( -3 \right )^{0}= -1$

$(-3^{0})=-1$

-1-(-1)=-1+1=0

Report an Error

Example Question #76 : Exponents

Simplify:

$3\sqrt{18} + 2\sqrt{50}$

Possible Answers:

$19\sqrt{2}$

$10\sqrt{2}$

$5\sqrt{68}$

$9\sqrt{2}$

$None\ of\ the\ above$

Correct answer:

$19\sqrt{2}$

Explanation:

$3\sqrt{18} = 3\sqrt{2\star 3^{2}} = 9\sqrt{2}$

Similarly $2\sqrt{50} = 2\sqrt{2\star 5^{2}} = 10\sqrt{2}$

So $9\sqrt{2} + 10\sqrt{2}= 19\sqrt{2}$

Report an Error

View PSAT Mathematics Tutors

Yongmao
Certified Tutor

Nankai University, Bachelor of Science, Chemistry. Washington University in St Louis, Doctor of Philosophy, Organic Chemistry.

View PSAT Mathematics Tutors

Rene Solo
Certified Tutor

University of the Philippines, Bachelor of Science, Mathematics. Prairie View A & M University, Master of Arts, Educational A...

View PSAT Mathematics Tutors

Shakeel
Certified Tutor

All PSAT Math Resources

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

Popular Subjects

MCAT Tutors in New York City, SAT Tutors in Philadelphia, Chemistry Tutors in Seattle, ACT Tutors in San Diego, Reading Tutors in New York City, Reading Tutors in Miami, Computer Science Tutors in Atlanta, French Tutors in Boston, Reading Tutors in Boston, Biology Tutors in Chicago

Popular Courses & Classes

LSAT Courses & Classes in Boston, SAT Courses & Classes in Washington DC, MCAT Courses & Classes in Houston, GRE Courses & Classes in Phoenix, SSAT Courses & Classes in Phoenix, ACT Courses & Classes in San Diego, GMAT Courses & Classes in Atlanta, Spanish Courses & Classes in Chicago, GMAT Courses & Classes in Denver, GMAT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

SAT Test Prep in Phoenix, GMAT Test Prep in Washington DC, LSAT Test Prep in Chicago, ACT Test Prep in San Diego, GRE Test Prep in Houston, GMAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Chicago, SAT Test Prep in Dallas Fort Worth, ACT Test Prep in Boston, SSAT Test Prep in Los Angeles

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 : How to add exponents

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #71 : Exponents

Example Question #93 : Exponents

Example Question #72 : Exponents

Example Question #73 : Exponents

Example Question #74 : Exponents

Example Question #3 : Exponents

Example Question #1 : Exponents

Example Question #75 : Exponents

Example Question #1 : Exponents

Example Question #76 : Exponents

All PSAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: