Back To Course

Math 101: College Algebra12 chapters | 94 lessons | 11 flashcard sets

Watch short & fun videos
**Start Your Free Trial Today**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 55,000 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.

We'll look at the five important exponent properties and an example of each. You can think of them as the order of operations for exponents. Learn how to handle math problems with exponents here!

We are going to talk about five exponent properties. You can think about them as the order of operations for exponents. Just like the order of operations, you need to memorize these operations to be successful. The five exponent properties are:

- Product of Powers
- Power to a Power
- Quotient of Powers
- Power of a Product
- Power of a Quotient

Let's look at the first one.

Here's the formula: (*x*^*a*)(*x*^*b*) = *x*^(*a* + *b*). When you multiply exponentials with the same base (notice that *x* and *x* are the same base), add their exponents (or powers).

Let me show you how that works. Let's say I have (*x*^2)(*x*^3). Well, *x*^2 is *x* times *x*, and *x*^3 is *x* times *x* times *x*. When we add all those *x*s up, we get *x*^5, which is the same thing as adding 3 + 2.

We can see from the formula we have (*x*^*a*)^*b*. When you have a power to a power, you multiply the exponents (or powers). Let me show you how this one works.

If I have (*x*^2)^4, which would be *x*^2 multiplied four times, or *x*^2 times *x*^2 times *x*^2 times *x*^2. Once again, we add all the exponents and get *x*^8, and *x*^8 is the same as *x*^(2 * 4), which is 8. Not too bad, right?

Remember, 'quotient' means 'division'.' The formula says (*x*^*a*) / (*x*^*b*) = *x*^(*a* - *b*). Basically, when you divide exponentials with the same base, you subtract the exponent (or powers).

Let me show you how this one works. Let's say I had (*x*^4) / (*x*^3). In the top (or numerator), we have *x* times *x* times *x* times *x*. In the bottom (or denominator), we have *x* times *x* times *x*. Hopefully, you remember that *x* divided by *x* is 1, so the *x*s cancel. So, *x* divided by *x* is 1, *x* divided by *x* is 1, and *x* divided by *x* is 1. So, when we cancel them, what are we left with? That's right: *x*^1, or just *x*. So (*x*^4) / (*x*^3) is just *x*^(4 - 3), which is *x*^1.

The formula says (*xy*)^*a* = (*x*^*a*) and (*y*^*a*). When you have a product of a power, you give each base its own exponent. Think about it as distribution putting the exponent with each base.

Let me show you how this one works. Let's say we had (*xy*)^2. That means we take *xy* and multiply it twice that means *xy* times *xy*. Well, that would give us two *x*s, or *x*^2, and two *y*s, or *y*^2. That is the same as if I distributed 2 to the *x*, getting *x*^2, and 2 to the *y*, getting *y*^2.

When we look at this formula, we have *x/y*, or a fraction raised to the *a* power, this gives us (*x*^*a*) / (*y*^*a*). When you have a quotient to a power, you give each base its own exponent. We think of it as the exponent being distributed to each part of the fraction, just like the last one, power of a product.

Let me show you how this one works. Let's say I have (*x* / *y*)^3. Remember, that means I'm going to take *x* / *y* and multiply it three times. That would be *x* / *y* times *x* / *y* times *x* / *y*. If we look at the top (or the numerator), we have *x* times *x* times *x*, or *x*^3. If we look at the bottom (or denominator), we have *y* times *y* times *y*, or *y*^3. That would give us (*x*^3) / (*y*^3), which is basically distributing 3 to the *x* and *y* .

Let's take a final minute to review the five properties.

**Product of a Power**: When you multiply exponentials with the same base, you add their exponents (or powers).**Power to a Power**: When you have a power to a power, you multiply the exponents (or powers).**Quotient of Powers**: When you divide exponentials with the same base, you subtract the exponents (or powers).**Power of a Product**: When you have a product of a power, you give each base its own exponent (or distribute the exponent to each base).**Power of a Quotient**: When you have a quotient to a power, you give each base its own exponent.

By the end of this lesson you'll know the five main exponent properties and understand examples of their applications.

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

Create
your account

Already a member? Log In

BackDid you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 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
1 in chapter 6 of the course:

Back To Course

Math 101: College Algebra12 chapters | 94 lessons | 11 flashcard sets

- What Are the Five Main Exponent Properties? 5:26
- How to Simplify Expressions with Exponents 4:52
- Rational Exponents 3:22
- 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

- Marketing 102: Intro to Digital Marketing
- Native Son Study Guide
- UExcel Financial Accounting: Study Guide & Test Prep
- DSST Money & Banking: Study Guide & Test Prep
- DSST Management Information Systems: Study Guide & Test Prep
- Understanding Receivables in Accounting
- Liabilities in Accounting
- Inventory Management in Accounting
- The Operating Cycle in Accounting
- Information Systems, Privacy & Security
- SBEC Technology Application Standards for Teachers
- How to Find Financial Aid for Teachers
- New Mexico State Standards for Science
- ELL Services in Massachusetts
- Publications for ESL Teachers
- WIDA Can Do Descriptors for Grades 9-12
- WV Next Generation Standards for Science

- 'The Horror! The Horror!' in Heart of Darkness
- What Is Marketing Strategy? - Examples & Objectives
- Labor Rate Variance: Definition & Formula
- The Book Thief Vocabulary
- Conditions of Freedom Essay Topics
- The Quiet American Essay Topics
- Pelvic Fracture: Complications, Treatment & Recovery
- Noun-Clause Activities & Games
- Quiz & Worksheet - Symbols & Symbolism in Orwell's 1984
- Quiz & Worksheet - Analyzing the Setting of Heart of Darkness
- Quiz & Worksheet - Understanding Multidomestic Strategy
- Quiz & Worksheet - Cult Leader Description
- Quiz & Worksheet - Configuration Management Process & Tools
- Regression & Correlation Flashcards
- Statistical Calculations for Business Flashcards

- DSST Lifespan Developmental Psychology: Study Guide & Test Prep
- AP Environmental Science: Homework Help Resource
- Quantitative Analysis: Tutoring Solution
- SAT Subject Test Mathematics Level 2: Tutoring Solution
- Middle School US History: Homeschool Curriculum
- AP World History - Ancient Times: Help and Review
- Holt McDougal Earth Science Chapter 21 - A Family of Planets
- Quiz & Worksheet - History & Goals of The World Bank
- Quiz & Worksheet - How to Identify & Calculate Averages
- Quiz & Worksheet - The Nuclear Arms Race & Cold War Politics
- Quiz & Worksheet - Confucianism's Founding & Influence
- Quiz & Worksheet - Plant Respiration

- Foreign Policy Powers of the President & Congress
- What Is GAAP? - Definition, Standards & Requirements
- How Much Does the MCAT Cost?
- James & the Giant Peach Lesson Plan
- Fantasy Writing Prompts
- Buoyancy Experiments for Kids
- What is a Good PSAT Score for a Sophomore?
- 2nd Grade Science Projects
- Plate Tectonics Activities for Kids
- How Hard is the CSET Math Exam?
- Special Education Resources for Parents
- Curriculum Vitae Template

Browse by subject