We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Exponents

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 5 6 Next →

Example Question #131 : Algebra Ii

$y=\frac{4x^2-2}{2x^3-27}$

What are the x-intercepts of the equation?

Possible Answers:

$x=\sqrt{2}, -\sqrt{2}$

$x=\frac{1}{\sqrt{2}}$

$x=\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}$

$x=\frac{2\sqrt{2}}{2}$

$x=\sqrt{2}$

Correct answer:

$x=\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}$

Explanation:

To find the x-intercepts, set the numerator equal to zero and solve.

0=4x^2-2

2=4x^2

$\frac{2}{4}=x^2$

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

$\sqrt{\frac{1}{2}}=\sqrt{x^2}$

We can simplify from here:

$\frac{\sqrt1}{\sqrt2}}=\sqrt{x^2}$

$\frac{1}{\sqrt2}}=\sqrt{x^2}$

Now we need to rationalize. Because we have a square root on the bottom, we need to get rid of it. Since $2=\sqrt{2}^2$ , we can multiply $\frac{1}{\sqrt2}*\frac{\sqrt{2}}{\sqrt{2}}$ to get rid of the radical in the denominator.

$\frac{1}{\sqrt2}*\frac{\sqrt{2}}{\sqrt{2}}=x$

$\frac{\sqrt{2}}{2}=x$

Since we took a square root, remember that our answer can be either positive or negative, as a positive squared is positive and a negative squared is also positive.

Report an Error

Example Question #132 : Algebra Ii

$y=\frac{x-3}{x^2-12}$

What are the y-intercepts of this equation?

Possible Answers:

$y=2\sqrt{3}$

y=0

y=4

There are no y-intercepts.

$y=\frac{1}{4}$

Correct answer:

$y=\frac{1}{4}$

Explanation:

To find the y-intercept, set x=0 and solve.

$y=\frac{x-3}{x^2-12}$

$y=\frac{(0)-3}{(0)^2-12}$

$y=\frac{-3}{-12}$

$y=\frac{1}{4}$

Report an Error

Example Question #133 : Algebra Ii

$y=\frac{x^2-64}{x+2}$

What are the y-intercepts of this equation?

Possible Answers:

There are no y-intercepts for the equation.

y=32

y=0

y=-32

y=-2

Correct answer:

y=-32

Explanation:

To find the y-intercept, set x=0 and solve.

$y=\frac{x^2-64}{x+2}$

$y=\frac{(0)^2-64}{0+2}$

$y=\frac{-64}{2}$

y=-32

Report an Error

Example Question #134 : Algebra Ii

$y=\frac{3x^2-5}{2x^2+7}$

What are the x-intercepts of the equation?

Possible Answers:

$x=\sqrt{\frac{5}{3}}, -\sqrt{\frac{5}{3}}$

x=0

x=1

$x=\sqrt{\frac{5}{3}}$

There are no horizontal asymptotes.

Correct answer:

$x=\sqrt{\frac{5}{3}}, -\sqrt{\frac{5}{3}}$

Explanation:

To find the x-intercepts, we set the numerator equal to zero and solve.

0=3x^2-5

5=3x^2

$\frac{5}{3}=x^2$

$\sqrt{\frac{5}{3}}=\sqrt{x^2}$

$\sqrt{\frac{5}{3}}=x$

However, the square root of a number can be both positive and negative.

Therefore the roots will be $x=\sqrt{\frac{5}{3}}, -\sqrt{\frac{5}{3}}.$

Report an Error

Example Question #135 : Algebra Ii

$y=\frac{x^2-64}{x+2}$

What are the x-intercepts of the equation?

Possible Answers:

There are no x-intercepts.

There are no real x-intercepts.

x=8, -8

x=-2

x=0

Correct answer:

x=8, -8

Explanation:

To find the x-intercepts, set the numerator equal to zero.

0=x^2-64

64=x^2

$\sqrt{64}=\sqrt{x^2}$

8,-8=x

Report an Error

Example Question #1 : Solving And Graphing Exponential Equations

Solve the equation for .

$\small 9^x=3^6$

Possible Answers:

$\small x=3$

$\small x=0$

$\small x=1$

$\small x=2$

Correct answer:

$\small x=3$

Explanation:

Begin by recognizing that both sides of the equation have a root term of .

$\small 9^x=3^6$

(3^2)^x=3^6

Using the power rule, we can set the exponents equal to each other.

$3^{(2*x)}=3^6$

$\small 2x=6$

$\small x=3$

Report an Error

Example Question #41 : Exponents

The population of a certain bacteria increases exponentially according to the following equation:

$P(t)=2000e^{^{2t}}$

where P represents the total population and t represents time in minutes.

How many minutes does it take for the bacteria's population to reach 48,000?

Possible Answers:

$\ln 12$

$\frac{2}{\ln 24}$

$\frac{2}{\log 24}$

$\frac{\log 24}{2}$

$\frac{\ln24}{2}$

Correct answer:

$\frac{\ln24}{2}$

Explanation:

The question gives us P (48,000) and asks us to find t (time). We can substitute for P and start to solve for t:

$48,000 = 2000e^{2t}$

$24 = e^{2t}$

Now we have to isolate t by taking the natural log of both sides:

$\ln 24 = \ln e^{2t}$

$\ln 24 = (2t)\ln e$

And since $\ln e = 1$ , t can easily be isolated:

$\ln 24 = 2t$

$\frac{\ln24}{2} = t$

Note: $\frac{\ln 24}{2}$ does not equal $\ln 12$ . You have to perform the log operation first before dividing.

Report an Error

Example Question #2 : Solving And Graphing Exponential Equations

Solve the equation for .

$\small 3^{2x}=81$

Possible Answers:

x=2

x=1

x=4

x=9

x=3

Correct answer:

x=2

Explanation:

Begin by recognizing that both sides of the equation have the same root term, .

$\small 3^{2x}=81$

$\small 3^{2x}=9^2$

$3^{2x}=(3^2)^2$

We can use the power rule to combine exponents.

$3^{2x}=3^4$

Set the exponents equal to each other.

2x=4

$\small x=2$

Report an Error

Example Question #42 : Exponents

Solve for :

x^3 - 9x =0

Possible Answers:

x = 3

$x = \{-3,0,3\}$

x = 0

$x = \{-3,3\}$

$x = \frac{1}{3}$

Correct answer:

$x = \{-3,0,3\}$

Explanation:

Pull an out of the left side of the equation.

$\rightarrow x(x^2 - 9) =0$

Use the difference of squares technique to factor the expression in parentheses.

$\rightarrow x(x+3)(x-3) =0$

Any number that causes one of the terms , x+3 , or x-3 to equal is a solution to the equation. These are , , and , respectively.

Report an Error

Example Question #1 : Graphing Exponential Functions

Find the -intercept(s) of $y=\frac{x^3+2x+8}{x^2-36}$ .

Possible Answers:

This function does not cross the -axis.

y=6

$y=\frac{2}{9}$

$y=-\frac{2}{9}$

y=8

Correct answer:

$y=-\frac{2}{9}$

Explanation:

To find the -intercept, set x=0 in the equation and solve.

$y=\frac{x^3+2x+8}{x^2-36}$

$y=\frac{(0)^3+2(0)+8}{(0)^2-36}$

$y=\frac{(0)+(0)+8}{(0)-36}$

$y=\frac{8}{-36}$

$y=-\frac{2}{9}$

Report an Error

← Previous 1 2 3 4 5 6 Next →

View Tutors

Eric
Certified Tutor

national autonomous university of Mexico , Doctorate (PhD), Mathematics .

View Tutors

Nicholle
Certified Tutor

The University of Texas at San Antonio, Bachelors, Chemistry. The University of Texas at San Antonio, Masters, Chemistry.

View Tutors

Chase
Certified Tutor

University of Memphis, Bachelor in Arts, Psychology.

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

French Tutors in New York City, GMAT Tutors in San Francisco-Bay Area, French Tutors in Chicago, Chemistry Tutors in Dallas Fort Worth, Reading Tutors in Seattle, English Tutors in Boston, English Tutors in Phoenix, MCAT Tutors in Denver, English Tutors in Los Angeles, Statistics Tutors in New York City

Popular Courses & Classes

GMAT Courses & Classes in Phoenix, Spanish Courses & Classes in Boston, SAT Courses & Classes in Los Angeles, SSAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Los Angeles, GRE Courses & Classes in Philadelphia, LSAT Courses & Classes in Washington DC, SAT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Seattle, ISEE Courses & Classes in New York City

Popular Test Prep

SSAT Test Prep in Atlanta, SAT Test Prep in Chicago, MCAT Test Prep in Houston, SAT Test Prep in Washington DC, LSAT Test Prep in Washington DC, ISEE Test Prep in Dallas Fort Worth, GMAT Test Prep in New York City, ISEE Test Prep in New York City, ACT Test Prep in Seattle, LSAT 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

High School Math : Exponents

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #131 : Algebra Ii

Example Question #132 : Algebra Ii

Example Question #133 : Algebra Ii

Example Question #134 : Algebra Ii

Example Question #135 : Algebra Ii

Example Question #1 : Solving And Graphing Exponential Equations

Example Question #41 : Exponents

Example Question #2 : Solving And Graphing Exponential Equations

Example Question #42 : Exponents

Example Question #1 : Graphing Exponential Functions

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: