Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Mathematical Relationships and Basic Graphs

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 #3313 : Algebra Ii

Simplify: $(\frac{2}{3})^{\frac{5}{2}}$

Possible Answers:

$\frac{11\sqrt6}{34}$

$\frac{2\sqrt6}{13}$

$\frac{7\sqrt5}{18}$

$\frac{4\sqrt6}{27}$

$\textup{This expression cannot be simplified.}$

Correct answer:

$\frac{4\sqrt6}{27}$

Explanation:

Use the product rule of exponents to simplify this term.

$(\frac{2}{3})^{\frac{5}{2}} = (\frac{2^{\frac{5}{2}}}{3^{\frac{5}{2}}})$

Rewrite this using radicals. The numerator represents the power that the radical is raised to. The denominator represents the root.

$(\frac{2^{\frac{5}{2}}}{3^{\frac{5}{2}}})= \frac{(\sqrt{2})^5}{(\sqrt{3})^5} = \frac{\sqrt{2}\cdot \sqrt{2}\cdot\sqrt{2}\cdot\sqrt{2}\cdot\sqrt{2}}{\sqrt{3}\cdot\sqrt{3}\cdot\sqrt{3}\cdot\sqrt{3}\cdot\sqrt{3}}$

Multiply the terms together. A radical multiplied by itself will be the integer inside the radical. The terms become:

$\frac{2\cdot 2 \cdot\sqrt2}{3\cdot3\cdot\sqrt3} = \frac{4\sqrt2}{9\sqrt{3}}$

Rationalize the denominator. Multiply the top and bottom by square root three.

$\frac{4\sqrt2}{9\sqrt{3}}\cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{4\sqrt6}{9\times 3}$

The answer is: $\frac{4\sqrt6}{27}$

Report an Error

Example Question #3314 : Algebra Ii

Which of the following is similar to $(3)^{\frac{7}{9}}$ ?

Possible Answers:

$(\frac{1}{3})^7$

$\frac{3^5}{9^7}$

$( \sqrt[7]{3})^9$

$(\frac{1}{3})^{\frac{7}{9}}$

$( \sqrt[9]{3})^7$

Correct answer:

$( \sqrt[9]{3})^7$

Explanation:

The fractional exponent will include both the power and the root. The numerator will represent the power that the quantity is raised to, and the denominator represents the root of the term.

Rewrite the expression in radical form.

$(3)^{\frac{7}{9}} =( \sqrt[9]{3})^7$

The answer is: $( \sqrt[9]{3})^7$

Report an Error

Example Question #3315 : Algebra Ii

Solve: $(\frac{1}{3})^{\frac{1}{2}}$

Possible Answers:

$\frac{\sqrt2}{3}$

$\frac{\sqrt6}{6}$

$\frac{\sqrt3}{9}$

$\frac{\sqrt3}{3}$

$\frac{\sqrt3}{2}$

Correct answer:

$\frac{\sqrt3}{3}$

Explanation:

Rewrite the half power with a radical.

$(\frac{1}{3})^{\frac{1}{2}} = \sqrt{\frac{1}{3}}$

Split the radical as two radicals.

$\sqrt{\frac{1}{3}} = \frac{\sqrt1}{\sqrt3}$

Rationalize the denominator. Multiply the top and bottom by square root three.

$\frac{\sqrt1}{\sqrt3}\cdot\frac{\sqrt3}{\sqrt3} =\frac{\sqrt3}{3}$

The answer is: $\frac{\sqrt3}{3}$

Report an Error

Example Question #181 : Exponents

Evaluate: $[-16^{\frac{3}{2}}]^{\frac{1}{2}}$

Possible Answers:

$\textup{The answer does not exist.}$

-8i

Correct answer:

Explanation:

In order to solve this, we will need to rewrite the inner term as a radical.

$[-16^{\frac{3}{2}}]^{\frac{1}{2}} = [-(\sqrt{16})^3] ^{\frac{1}{2}}$

Simplify the inner term.

$[-64]^{\frac{1}{2}} = \sqrt{-64}$

The answer is:

Report an Error

Example Question #182 : Exponents

Solve: $289^{\frac{3}{2}}-27^{\frac{2}{3}}$

Possible Answers:

4904

1825

1000

262

196

Correct answer:

4904

Explanation:

We can rewrite both terms using the radicals. The denominator of a fractional exponent is the index of the root. The numerator of the fraction is the power of the quantity.

Rewrite the terms.

$289^{\frac{3}{2}}-27^{\frac{2}{3}} =( \sqrt{289})^3 - (\sqrt[3]{27})^2$

Simplify the radicals and solve.

$289^{\frac{3}{2}}-27^{\frac{2}{3}} =(17)^3 - (3)^2 = 4913 -9 = 4904$

The answer is: 4904

Report an Error

Example Question #3318 : Algebra Ii

Simplify:

$\frac{(x^2)(x^{\frac{1}{2}}y^9)}{x^{-\frac{4}{3}}y^5}$

Possible Answers:

$\frac{y^4}{x^{\frac{23}{6}}}$

$\frac{x^{\frac{23}{6}}}{y^4}$

$x^{\frac{8}{3}}y^9$

$x^\frac{23}{6}y^4$

Correct answer:

$x^\frac{23}{6}y^4$

Explanation:

Start by simplifying the numerator. Since two terms with the same base are being multiplied, add the exponents.

$\frac{(x^2)(x^{\frac{1}{2}}y^9)}{x^{-\frac{4}{3}}y^5}=\frac{x^{\frac{5}{2}}y^9}{x^{-\frac{4}{3}}y^5}$

Now, when terms with the same bases are divided, subtract the exponent from the denominator from the exponent in the numerator.

The exponent for is

$\frac{5}{2}-(-\frac{4}{3})=\frac{23}{6}$

The exponent for is

9-5=4

So then,

$\frac{(x^2)(x^{\frac{1}{2}}y^9)}{x^{-\frac{4}{3}}y^5}=\frac{x^{\frac{5}{2}}y^9}{x^{-\frac{4}{3}}y^5}=x^{\frac{23}{6}}y^4$

Report an Error

Example Question #1 : Applications

Twelve years ago, your grandma put money into a savings account for you that earns $7.5\%$ interest annually and is continuously compounded. How much money is currently in your account if she initially deposited $\$10,000$ and you have not taken any money out?

Possible Answers:

$24,596

$10,778

$8,103

$21,170

$81,030

Correct answer:

$24,596

Explanation:

1. Use $x=Pe^{rt}$ where is the current amount, is the interest rate, is the amount of time in years since the initial deposit, and is the amount initially deposited.

r=0.075

P=$10,000

t=12

2. Solve for

$x=Pe^{rt}$

$x=10,000e^{(0.075\cdot12)}$

x=24,596.03

You currently have $24,596 in your account.

Report an Error

Example Question #2 : Using E

Solve for

$5^{x}=125^{3x-1}$

Possible Answers:

$\frac{3}{8}$

$-\frac{3}{8}$

Correct answer:

$\frac{3}{8}$

Explanation:

Step 1: Achieve same bases

$5^{x}=125^{3x-1}$

$5^{x}=(5^{3})^{3x-1}$

$5^{x}=5^{9x-3}$

Step 2: Drop bases, set exponents equal to eachother

x=9x-3

Step 3: Solve for x

-8x=-3

$x=\frac{3}{8}$

Report an Error

Example Question #3 : Using E

Solve for

$2^{-x}=4$

Possible Answers:

Correct answer:

Explanation:

Step 1: Achieve same bases

$2^{-x}=4$

$2^{-x}=2^{2}$

Step 2: Drop bases, set exponents equal to eachother

-x=2

Step 3: Solve for

x=-2

Report an Error

Example Question #2 : Using E

Solve for

$4^{x}=2^{5x-3}$

Possible Answers:

$\frac{5}{3}$

Correct answer:

Explanation:

Step 1: Achieve same bases

$4^{x}=2^{5x-3}$

$(2^{2})^{x}=2^{5x-3}$

$2^{2x}=2^{5x-3}$

Step 2: Drop bases and set exponents equal to eachother

2x=5x-3

Step 3: Solve for

-3x=-3

x=1

Report an Error

View Algebra 2 Tutors

Ravi
Certified Tutor

Indian Institute of Technology - Mumbai, Bachelor of Technology, Mechanical Engineering. University of Cincinnati-Main Campus...

View Algebra 2 Tutors

Dilip
Certified Tutor

University of Calcutta, Bachelor of Science, Physics. Indiana Institute of Technology, Master of Science, Physics.

View Algebra 2 Tutors

Matthew
Certified Tutor

Bluffton University, Bachelor of Education, Mathematics. Bluffton University, Masters in Education, Education.

All Algebra II Resources

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

Popular Subjects

French Tutors in San Francisco-Bay Area, Reading Tutors in San Diego, Physics Tutors in Boston, French Tutors in Dallas Fort Worth, SAT Tutors in Miami, Calculus Tutors in Denver, Chemistry Tutors in Boston, Computer Science Tutors in Los Angeles, Spanish Tutors in San Francisco-Bay Area, SSAT Tutors in Boston

Popular Courses & Classes

GMAT Courses & Classes in Denver, SSAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Washington DC, GMAT Courses & Classes in Houston, ISEE Courses & Classes in Chicago, SAT Courses & Classes in Washington DC, MCAT Courses & Classes in Boston, ACT Courses & Classes in Boston, MCAT Courses & Classes in Los Angeles, MCAT Courses & Classes in Phoenix

Popular Test Prep

MCAT Test Prep in Denver, GRE Test Prep in New York City, GMAT Test Prep in New York City, LSAT Test Prep in Los Angeles, GMAT Test Prep in Denver, LSAT Test Prep in Miami, GMAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Chicago, ACT Test Prep in Philadelphia, GMAT Test Prep in Seattle

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 : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #3313 : Algebra Ii

Example Question #3314 : Algebra Ii

Example Question #3315 : Algebra Ii

Example Question #181 : Exponents

Example Question #182 : Exponents

Example Question #3318 : Algebra Ii

Example Question #1 : Applications

Example Question #2 : Using E

Example Question #3 : Using E

Example Question #2 : Using E

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: