Back To Course

Math 101: College Algebra13 chapters | 102 lessons | 11 flashcard sets

Are you a student or a teacher?

Try Study.com, risk-free

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Login here for access

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Kathryn Maloney*

Kathryn teaches college math. She holds a master's degree in Learning and Technology.

Simplifying expressions with rational exponents is so easy. In fact, you already know how to do it! We simply use the exponent properties but with fractions as the exponent!

Rational exponents follow exponent properties except using fractions.

Review of exponent properties - you need to memorize these. Just can't seem to memorize them? Have you tried flashcards? They work fantastic, and you can even use them anywhere!

**Product of Powers**:*x**a***x**b*=*x*(*a*+*b*)**Power to a Power**: (*x**a*)*b*=*x*(*a***b*)**Quotient of Powers**: (*x**a*)/(*x**b*) =*x*(*a*-*b*)**Power of a Product**: (*x**y*)*a*=*x**a**y**a***Power of a Quotient**: (*x*/*y*)*a*=*x**a*/*y**a***Negative Exponent**:*x*(-*a*) = 1 /*x**a***Zero Exponent**:*x*0 = 1

Putting the exponent rules to work with exponent properties...

*y*(1/2) * *y*(1/3)

For this one, we're going to follow the product of powers. Remember, when we multiply, we add their exponents.

1/2 + 1/3 = 5/6

So the answer is going to be *y*(5/6).

Simplify: *x*(3/5) / *x*(2/3)

For this one, we're going to use the quotient of powers. Remember, when we divide, we subtract their exponents. So, we're going to have:

*x*(3/5 - 2/3)

3/5 - 2/3 = -1/15

So our answer is *x*(-1/15).

Simplify: *x*(-2/7)

For this one, we're going to use the negative exponents property. Remember, when we have a negative exponent, we flip it. If it's in the numerator, we flip it to the denominator, which is in this case.

So our answer is going to be 1 / (*x*(2/7)).

Simplify: (*x*(4/5))(3/4)

In this one, we have power to a power. We're going to have (*x*(4/5))(3/4), so we're going to multiply 4/5 * 3/4 which is 12/20. We need to reduce our fractions when we're going to get our final answer. 12/20 reduces to 3/5.

So our answer is going to be *x*(3/5).

Putting multiple exponent rules to work with exponent properties... Simplify using positive exponents. Always reduce the fractions to lowest terms.

First we're going to simplify the power to a power. So now we'll have:

Write like terms over each other, if necessary. Well, we already have the *p*'s over the *p*'s and the *q*'s over the *q*'s. There's no need to simplify fractions now. We're going to go right to simplifying quotient of powers. Remember, when we divide, we subtract their exponents. So we have:

*p*(2/6 - 1/2) * *q*(6/3 - 1/2)

That gives us:

*p*(-1/6) * *q*(9/6)

Next we need to reduce the fractions because we're almost to our answer. So we'll have:

*p*(-1/6) * *q*(3/2)

We want to rewrite these using positive exponents. Remember, if it's negative in the numerator, it flips to the denominator. So our final answer's going to be:

*q*(3/2) / *p*(1/6)

Simplify using positive exponents. Always reduce the fractions to lowest terms. We're going to have:

We're going to simplify power to a power. So we'll have:

Remember, power to a power means to multiply the exponents. Next, let's write like terms over each other. We already have 23 over 82 and *m*(6/3) over *m*(2/6). So let's move to the next step. There's no need to simplify fractions just yet, so we're going to simplify quotient of powers. Remember, when we divide, we subtract. So now we're going to have:

8/64 * *m*(6/3 - 2/6)

Well, 8/64 is 1/8. *m* to the 6/3 - 2/6 is *m* to the 10/6. So it turns out that our final answer is:

*m*(5/3) / 8

We won't touch the improper fraction in this video. We're just simplifying rational exponents.

Simplify using positive exponents. Always reduce fractions to lowest terms.

First we're going to simplify power to a power. Remember, power to a power means to multiply the exponents. That'll give us:

Next, if we need to, write like terms over each other. There's no need to simplify fractions now. We're going to move to quotient of powers. Remember, when we divide, we subtract their exponents. So that's going to give us:

*p*(3/10 - (-2/10))*q*(-1/4 - (-1/4))

So let's keep simplifying.

*p*(5/10)*q*(0)

The zero exponent says *q*0 equals 1. Now we need to reduce our fraction 5/10. That's going to give us our answer:

*p*(1/2)

Review radical to rational fraction formula...

The *b*th root of *x**a* = *x*(*a*/*b*)

The index is the denominator. The exponent is the numerator. What happens when the expression has radicals?

- Change the radicals to rational exponents
- Follow exponent rules

(third root of *x*)(fifth root of *x*4)

First we need to change to rational exponents, so we're going to have:

*x*(1/3) * *x*(4/5)

Did you remember the denominator is the index number and the numerator is the radicand exponent? Following our exponent rules, we're going to do a product of powers. Remember, when we multiply, we add their exponents. So we're going to have:

*x*(1/3 + 4/5)

Well, 1/3 plus 4/5 is 17/15. So our answer's going to be:

*x*(17/15)

Remember, we need to change the rational exponent back into a radical expression.

*x*(17/15) = 15th root of *x*17

Rational exponents follow the exponent rules. Remember to reduce fractions as your final answer, but you don't need to reduce until the final answer. For operations on radical expressions, change the radical to a rational expression, follow the exponent rules, then change the rational expression back to a radical expression.

By the end of this lesson you'll be able to simplify expressions with rational exponents.

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackWhat teachers are saying about Study.com

Already registered? Login here for access

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
5 in chapter 6 of the course:

Back To Course

Math 101: College Algebra13 chapters | 102 lessons | 11 flashcard sets

- What Are the Five Main Exponent Properties? 5:26
- How to Define a Zero and Negative Exponent 3:13
- How to Simplify Expressions with Exponents 4:52
- Rational Exponents 3:22
- Simplifying Expressions with Rational Exponents 7:41
- How to Add, Subtract and Multiply Polynomials 6:53
- How to Divide Polynomials with Long Division 8:05
- How to Use Synthetic Division to Divide Polynomials 6:51
- Dividing Polynomials with Long and Synthetic Division: Practice Problems 10:11
- Go to Exponents and Polynomials

- Go to Functions

- AFOQT Information Guide
- ACT Information Guide
- Computer Science 335: Mobile Forensics
- Electricity, Physics & Engineering Lesson Plans
- Teaching Economics Lesson Plans
- FTCE Middle Grades Math: Connecting Math Concepts
- Social Justice Goals in Social Work
- Developmental Abnormalities
- Overview of Human Growth & Development
- ACT Informational Resources
- AFOQT Prep Product Comparison
- ACT Prep Product Comparison
- CGAP Prep Product Comparison
- CPCE Prep Product Comparison
- CCXP Prep Product Comparison
- CNE Prep Product Comparison
- IAAP CAP Prep Product Comparison

- What's the Difference Between Polytheism and Monotheism?
- Ethnic Groups in America
- What Are the 5 Ws in Writing? - Uses & Examples
- Phenol: Preparation & Reactions
- Plant Life Cycle Project Ideas
- Medieval Castle Project Ideas
- Samurai Project Ideas
- Quiz & Worksheet - Solvay Process
- Quiz & Worksheet - Kinds of Color Wheels
- Quiz & Worksheet - Understanding Abbreviations
- Quiz & Worksheet - Act & Rule Utilitarianism Comparison
- Analytical & Non-Euclidean Geometry Flashcards
- Flashcards - Measurement & Experimental Design
- Anti-Bullying Guide | Stop Bullying in Schools
- Punctuation Worksheets

- High School Algebra I: Homeschool Curriculum
- Environmental Science 101: Environment and Humanity
- High School Trigonometry: Tutoring Solution
- 12th Grade English Textbook
- Saxon Calculus Homeschool: Online Textbook Help
- Middle School Language Arts: Using Source Materials
- Overview of Literary Analysis
- Quiz & Worksheet - How Business Can Improve the Standard of Living
- Quiz & Worksheet - Comparing & Contrasting Ideas in a Text
- Quiz & Worksheet - Project Risk Management Plan
- Quiz & Worksheet - Economic Benefits
- Quiz & Worksheet - C2C e-Commerce Business Model

- Development & Maintenance of Interest Groups
- Oxygenic and Anoxygenic Phototrophs: Definition and Examples
- Reading Food Labels Lesson Plan
- Recycling Activities & Games for Kids
- Best Apps for the Classroom
- Civil Rights Activities for Kids
- Response to Intervention (RTI) in Ohio
- Enlightenment Lesson Plan
- Study.com's Top Online Leadership Training Courses
- Louisiana Alternative Teacher Certification
- Cinco De Mayo Activities for Kids
- Resources for Teachers of English Language Learners

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject