Back To Course

Math 101: College Algebra12 chapters | 95 lessons | 11 flashcard sets

Are you a student or a teacher?

Start Your Free Trial To Continue Watching

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.

Free 5-day trial
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.

In this video, we will put all of the exponent properties we have learned together. Don't let lots of numbers and letters confuse you! Simplifying exponents can be easy and fun!

Let's review the exponent properties:

**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**: (*xy*)^*a*=*x*^*a**y*^*a***Zero Property**:*x*^0 = 1

If you're having problems memorizing these properties, I suggest using flash cards. Flash cards are a fantastic and easy way to memorize topics, especially math properties.

So, let's get started!

Simplify is the same as reducing to lowest terms when we talk about fractions. Simplifying these terms using positive exponents makes it even easier for us to read.

Our first expression has *x*^3*y*^8 / *y*^3*x*^7. The first step I like to do is put the like terms on top of each other. On the top, I have *x*^3*y*^8. In the denominator, I want the *x*s over each other and the *y*s over each other, so I write *x*^7*y*^3.

My next step is to split these up using multiplication. This step is important when you first begin because you can see exactly what we are doing. Splitting the multiplication gives us *x*^3 / *x*^7 times *y*^8 / *y*^3.

Next step - look at each part individually. Since we have *x*^3 divided by *x*^7, we subtract their exponents. This gives us *x*^3-7. Since we have *y*^8 divided by *y*^3, we subtract their exponents. This gives us *y*^8-3. This will give us *x*^3-7, which is -4 and *y*^8-3, which is 5.

Remember, we're simplifying using positive exponents, so we need to change *x*^-4. We know from our exponent properties that *x*^-4 is 1 / *x*^4 times *y*^5. Well, 5 is positive, so we don't need to change it.

My last step is to multiply. Our final, simplified answer is *y*^5 / *x*^4. This is our simplified answer with positive exponents.

Let me show you another one. This time we have 5*x*^2*y*^9 / 15*y*^9*x*^4. Let's rewrite this with like terms over each other: 5/15 times *x*^2 / *x*^4 times *y*^9/*y*^9

We start at the beginning. 5/15 reduces to 1/3. Next, *x*^2 divided by *x*^4 is *x*^(2-4). *y*^9 divided by *y*^9 is *y*^(9-9). Let's keep simplifying. We have 1/3 times *x*^(2-4), which is -2, times *y*^(9-9), which is *y*^0. This gives us 1/3 times 1/*x*^2 times 1. Multiplying straight across, our final answer is 1/3*x*^2.

This is our answer simplified using positive exponents.

There are a lot of letters and numbers here, but don't let them trick you. If we keep separating the terms and following the properties, we'll be fine.

Our first step is to simplify (2*p*)^3. We distribute the exponent to everything in the parenthesis. This will give us (8*p*)^3*q*^4 in the bottom or denominator, but our top or numerator will stay the same.

Next, we separate them into multiplication: 16/8 times *p*/*p*^3 times *q*^2 / *q*^4 times *r*^9.

Here's the fun part, simplify. 16/8 is 2/1 times *p*^(1-3) times *q*^(2-4) times *r*^9.

We're almost done: 2 times *p*^(1-3) is -2, times *q*^(2-4), which is *q*^(-2) times *r*^9.

We are asked to simplify using positive exponents: *p*^(-2) is the same as 1/*p*^2; *q*^(-2) is the same 1/*q*^2.

Finally, our last step - multiplying the fractions straight across. Our final answer is *r*^9 / *p*^2*q*^2. This is in simplified form using positive exponents.

Remember, it will take time and practice to be good at simplifying fractions.

After this lesson you'll be able to simplify expressions with 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

BackDid 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
3 in chapter 6 of the course:

Back To Course

Math 101: College Algebra12 chapters | 95 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
- Simplifying Expressions with Rational Exponents 7:41
- How to Graph Cubics, Quartics, Quintics and Beyond 11:14
- 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

- Computer Science 336: Network Forensics
- Computer Science 220: Fundamentals of Routing and Switching
- Global Competency Fundamentals & Applications
- Introduction to the Principles of Project Management
- Praxis Elementary Education: Reading & Language Arts - Applied CKT (7902): Study Guide & Practice
- Practical Applications for Business Ethics
- Practical Applications for Marketing
- Practical Applications for HR Management
- Practical Applications for Organizational Behavior
- Analyzing Texts Using Writing Structures
- MBLEx Prep Product Comparison
- AEPA Prep Product Comparison
- ASCP Prep Product Comparison
- NCE Prep Product Comparison
- TASC Test Score Information
- What is the TASC Test?
- Praxis Prep Product Comparison

- Diclofenac vs. Ibuprofen
- Developing & Managing a High-Quality Library Collection
- Library Space Planning
- Literacy Strategies for Teachers
- Arithmetic Operations in R Programming
- Practical Application: Understanding Employee Behavior
- Positive Global Outcomes of Global Competence
- Practical Application: Color Wheel Infographic
- Quiz & Worksheet - Developing a Learner-Centered Classroom
- Quiz & Worksheet - Technology for Teaching Reading
- Quiz & Worksheet - Pectoralis Major Anatomy
- Quiz & Worksheet - Oral & Written Communication Skills
- Quiz & Worksheet - How to Teach Reading to ELL Students
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies

- Intro to Business: Help and Review
- Psychology 103: Human Growth and Development
- Common Core Math - Functions: High School Standards
- DSST The Civil War & Reconstruction: Study Guide & Test Prep
- CSET Science Subtest I - General Science (215): Practice & Study Guide
- Geometry Basics for Precalculus: Tutoring Solution
- Graph Symmetry: Tutoring Solution
- Quiz & Worksheet - National Environmental Policy Act & Other Laws
- Quiz & Worksheet - Multiple Alleles & Codominant Genes
- Quiz & Worksheet - How to Use Indicator Bacteria to Monitor Public Water Supplies
- Quiz & Worksheet - Electrical Resistance
- Quiz & Worksheet - Cultural Perceptions of Power in Organizations

- Common Issues with Middle/Secondary School Children
- Solving Systems of Equations by Graphing Calculator
- Frindle Lesson Plan
- ESL Reading Comprehension Tests
- How to Pass the PSAT
- Homeschool Laws by State
- Homeschool vs. Public School Statistics
- Scientific Method Lesson Plan
- Kansas Science Standards for 4th Grade
- Texas Teacher Evaluation System
- Best LSAT Prep Course
- Teacher Retirement System of Texas Withdrawal

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

Browse by subject