Back To Course

Math 101: College Algebra12 chapters | 95 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.

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

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
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 109: Introduction to Programming
- Introduction to HTML & CSS
- Introduction to JavaScript
- Computer Science 332: Cybersecurity Policies and Management
- Introduction to SQL
- Building the United States After the American Revolution
- Manifest Destiny & the American Civil War
- Imperialism & International Relations in the 19th & 20th Centuries
- Western Civilization from 1945-1973
- The Development of the Hindu, Buddhist, Confucian, & Judeo-Christian Faiths
- CEOE Test Cost
- PHR Exam Registration Information
- Claiming a Tax Deduction for Your Study.com Teacher Edition
- What is the PHR Exam?
- Anti-Bullying Survey Finds Teachers Lack the Support They Need
- What is the ASCP Exam?
- ASCPI vs ASCP

- Iroquois Culture, Traditions & Facts
- What are Diastereomers? - Definition, Examples & Separation
- Convergent Sequence: Definition, Formula & Examples
- Mauryan Empire Art & Culture
- Singing Lesson Plan
- Arrays & Strings in JavaScript: Conversion & String Methods
- Heuristic Methods in AI: Definition, Uses & Examples
- Quiz & Worksheet - Multi-Dimensional Arrays in C
- Quiz & Worksheet - Functions & Parameters Overview
- Quiz & Worksheet - Speed, Velocity & Acceleration
- Quiz & Worksheet - Testing to Identify a Gas
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies
- 5th Grade Math Worksheets & Printables
- Sentence Structure Worksheets

- Middle School Earth Science: Homework Help Resource
- Cambridge Pre-U Mathematics - Short Course: Practice & Study Guide
- AP European History Textbook
- GRE Prep: Tutoring Solution
- Holt Chemistry: Online Textbook Help
- Chapter 1: Essentials of Geometry
- HiSET: Measuring the Economy
- Quiz & Worksheet - Romantic Painting in America vs. Europe
- Quiz & Worksheet - Rembrandts Self-Portraiture
- Quiz & Worksheet - Being a Positive Influence at Work
- Quiz & Worksheet - Supervising Reading Programs
- Quiz & Worksheet - Food in the Neolithic Age

- The Role of Native Language in Second Language Acquisition
- Misery Index: Purpose & Calculation
- Kentucky Science Standards for 4th Grade
- How Organizations Can Leverage Employee Education Benefits to Attract and Retain Top Talent
- Homeschooling in Canada
- Mexican-American War Lesson Plan
- WV College & Career Readiness Standards for Social Studies
- Third Grade Georgia Science Standards
- Homeschooling in Hawaii
- Missouri State Standards for Math
- Engineering Degrees 101
- Actuarial Science Exams

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

Browse by subject