Back To Course

Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

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 70,000 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:
*Jennifer Beddoe*

There are certain rules that govern working with exponential expressions. This lesson deals with the rule for multiplying exponential expressions. It will describe the rule and give some examples of how it works.

An exponent is a number written as a superscript to another number. It looks like this:

The **exponent** of a number tells you how many times to multiply that number to itself. So, in the above example, 2^3 means 2*2*2, which is equal to 8.

Using the **carat** (^) symbol is another way to write an exponent that can be easier when typing.

Exponents make large multiplication problems easier to write. So instead of writing 9*9*9*9*9*9, you can just write: 9^6.

There are certain laws that govern working with exponents. One of these rules has to do with multiplying expressions that contain exponents.

When you have two exponential expressions that have the same base, you can easily multiply them together. All you have to do is add the exponents.

Here's an example:

(3^2)*(3^5)

To simplify this expression, just add the exponents:

2 + 5 = 7, and your answer is:

3^7

Let's take a look at how this works.

If we write out the multiplication of each exponent, we get

(3*3)*(3*3*3*3*3), which equals:

3*3*3*3*3*3*3

To write this with exponents, we just count up the number of threes - there are 7 of them, so the simplified answer is 3^7.

This simplification works with all exponential expressions where the base is the same for each term.

Let's try another one

Simplify: (*x*^3)*(*x*^6)

To simplify this expression, just add the exponents:

3 + 6 = 9, so (*x*^3)*(*x*^6) = *x*^9

The rule also applies if one or more of the exponents are negative.

Simplify (4^-3)*(4^5)

Again, just add the exponents.

-3 + 5 = 2

So, (4^-3)*(4^5) = 4^2

If the terms you are working with have different bases, there is not much you can do to simplify the expression.

For example:

Simplify: (3^2)*(*x*^4)

Since the bases for each term (3 and *x*) are different, nothing can be done to simplify this expression, and you are left with (3^2)(*x*^4).

Simplify: (*b*^5)(*c*^3)

The same rule applies to this example. Because the bases are not the same, nothing can be done to simplify the expression. The answer is (*b*^5)(*c*^3).

The only exception to this rule is if both the bases are numbers. Then, to simplify, you can simplify each term and multiply them together.

For example, Simplify (2^3)*(6^2)

2^3 = 8 and 6^2 = 36

You can simplify this problem by multiplying 8 and 36.

8 * 36 = 288

Exponents are numbers written as superscripts that tell you how many times to multiply the base number to itself. In order to multiply two exponential expressions together, they must have the same base, and all you need to do is add the exponents. This works if the exponents are positive or negative, but only if the bases are the same. If the terms have different bases, there is not much that can be done to simplify.

At the end of this lesson you should be able to:

- Understand and use the (^) symbol
- Simplify multiplication equations using exponents
- Simplify exponential equations with the same bases

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
5 in chapter 5 of the course:

Back To Course

Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

- How to Use Exponential Notation 2:44
- Scientific Notation: Definition and Examples 6:49
- Simplifying and Solving Exponential Expressions 7:27
- Exponential Expressions & The Order of Operations 4:36
- Multiplying Exponential Expressions 4:07
- The Power of Zero: Simplifying Exponential Expressions 5:11
- Negative Exponents: Writing Powers of Fractions and Decimals 3:55
- Power of Powers: Simplifying Exponential Expressions 3:33
- Go to High School Algebra: Exponents and Exponential Expressions

- ORELA Essential Academic Skills: Practice & Study Guide
- Math 108: Discrete Mathematics
- ORELA Elementary Education - Subtest II: Practice & Study Guide
- ORELA Special Education: Practice & Study Guide
- MTEL Academically Advanced (52): Test Prep & Study Guide
- Relations Between Labor & Management
- Introduction to Logic & Proofs
- Sets & Functions in Discrete Math
- Binomial Probability
- Counting Rules, Combinations & Permutations
- How to Request a CLEP Transcript
- CLEP Exam Dates & Testing Center Locations
- CLEP Scoring System: Passing Scores & Raw vs. Scaled Score
- Continuing Education Opportunities for Molecular Biology Technologists
- WV College & Career Readiness Standards for Social Studies
- Common Core State Standards in Ohio
- Resources for Assessing Export Risks

- Required Rate of Return (RRR): Formula & Calculation
- Fixed Phrases: Definition, Examples & Practice
- Why Do Workers Join Unions? - Benefits & Reasons
- Rigid Motion in Geometry
- Professional Organizations & Literature for Media Specialists
- History of Wat Rong Khun
- Roger de La Fresnaye: Biography, Artwork & Cubism
- Jacobean Era Furniture: History & Characteristics
- Quiz & Worksheet - Animal Population Size
- Quiz & Worksheet - Psychoanalyst Anna Freud
- Quiz & Worksheet - Potassium Chromate
- Quiz & Worksheet - Understsanding Transaction Processing Systems
- Quiz & Worksheet - Decomposing Numbers
- Tourism Marketing Flashcards
- Tourism Economics Flashcards

- NY Regents Exam - Integrated Algebra: Tutoring Solution
- Common Core ELA - Writing Grades 11-12: Standards
- ACT Prep: Help and Review
- SAT Prep: Practice & Study Guide
- Common Core Math Grade 7 - Ratios & Proportional Relationships: Standards
- Algebra II - Absolute Value Review: Tutoring Solution
- AP World History - The Medieval Warm Period: Help and Review
- Quiz & Worksheet - Organization & Goals of American States
- Quiz & Worksheet - Angle-Angle-Side Theorem
- Quiz & Worksheet - Portable Media Devices & Cell Phone Technology
- Quiz & Worksheet - Researching the Brain and Behavior
- Quiz & Worksheet - GRE Issue Essay

- Social Unrest: Definition & Overview
- Guillaume Dufay: Biography & Music
- Female Detective Books
- 3rd Grade Math Projects
- Engineering Internships for High School Students
- What is the STAR Reading Test?
- What is Micro Credentialing?
- Common Core State Standards in Missouri
- How to Pass the TOEFL Exam
- Praxis Tests in Tennessee
- How to Pass a Math Test
- The Best Free CLEP Test Prep

Browse by subject