Back To Course

Supplemental Math: Study Aid1 chapters | 19 lessons

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*

The zero exponent rule states that any term with an exponent of zero is equal to one. This lesson will go into the rule in more detail, explaining how it works and giving some examples. There will also be a quiz to test your knowledge.

The zero exponent rule is one of the rules that will help you simplify exponents. Let's first define some terms as they relate to exponents. When you have a number or variable raised to a power, the number (or variable) is called the **base**, while the superscript number is called the **exponent**, or **power**.

Usually, you'll see this written with the base being a normal-size number (or letter, if you're working with a variable). The exponent will be in a slightly smaller font, raised a little up above and to the right of the base. However, in some formats, like this one, you'll see the base, a mark called a caret that looks like an inverted V, and then the exponent. So if you have a base of 2 and an exponent of 3, we'll write that out here as 2^3 = 8.

Now that you know the terms, let's go back to the zero exponent rule. The **zero exponent rule** basically says that any base with an exponent of zero is equal to one. For example:

*x*^0 = 1- 5^0 = 1
- 3^0 *
*a*^0 = 1 - 7
*m*^0 = 7 * 1 = 7. The 7 is its own term, and in this problem, it's being multiplied by the second term (*m*^0). That's why the entire expression is not equal to 1. The only portion that will be equal to 1 is the portion with the exponent of 0.

There is a solid mathematical reason for why this works. It's not just some arbitrary rule that mathematicians made up to keep algebra students confused. In order to explain the zero exponent rule, we need to back up a bit and talk about the rule for dividing exponents.

When you are dividing exponents, you subtract the exponents in the denominator from the exponents in the numerator. As with other operations, the base must be the same before you can combine exponents. For example, *y*^5 / *y*^3 = *y*^2 because 5 - 3 = 2.

How does this relate to the zero rule? Well, if you have a division problem that looks like this - *y*^3 / *y*^3 - and you use the division rule, you get *y*^0 because 3 - 3 = 0. We also know from simple mathematics that anything divided by itself is one:

- 2 / 2 = 1
- 5436 / 5436 = 1
*x*/*x*= 1*y*^3 /*y*^3 = 1

So, because *y*^3 / *y*^3 = 1 (according to mathematics) and *y*^3 / *y*^3 = *y*^0 (according to the division rule), you can also say that *y*^0 = 1. In other words, 1 = *y*^3 / *y*^3 = *y*^0; therefore 1 = *y*^0.

The only case when this would not be true is if *y* = 0. If the denominator of a fraction is 0, then the fraction is undefined. Therefore, substituting 0 for *y* in the example we have been using would give us 0^3 / 0^3. This would not equal 1 but would be undefined because of the 0 in the denominator.

Here are a few more quick examples so you can see the zero exponent rule in practice:

*t*^0 = 1- (
*x*^2 **y*^2) / (*x*^2 **y*^2) =*x*^(2 - 2) **y*^(2 - 2) =*x*^0 **y*^0 = 1 - 6
*m*^0*n*^2 = 6*n*^2

There are many rules that are used to simplify expressions in mathematics. The **zero exponent rule** is used to simplify terms with zero exponents. The rule states that any term with zero as an **exponent** is equal to one. The only time this is not true is if the **base** is zero. If the base is zero, the proof would require the zero to be in the denominator of a fraction. This result would be undefined. In summary, *x*^0 = 1, and *x* does not equal 0.

As this lesson concludes, you might have the skills necessary to:

- State and implement the zero exponent rule
- Solve an exponential equation that has zeros as exponents

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
8 in chapter 1 of the course:

Back To Course

Supplemental Math: Study Aid1 chapters | 19 lessons

- Less Than Symbol in Math: Problems & Applications 4:10
- What are 2D Shapes? - Definition & Examples 4:35
- Trapezoid: Definition, Properties & Formulas 3:58
- What is Surface Area? - Definition & Formulas 5:56
- Using Parentheses in Math: Rules & Examples 3:58
- Universal Set in Math: Definition, Example & Symbol 6:03
- Complement of a Set in Math: Definition & Examples 5:59
- Zero Exponent: Rule, Definition & Examples 4:32
- What is Simplest Form? - Definition & How to Write Fractions in Simplest Form 5:49
- What is Slope? - Definition & Formulas 7:10
- Skewed Distribution: Examples & Definition 5:09
- Change Of Base Formula: Logarithms & Proof 4:54
- Transformations in Math: Definition & Graph 6:27
- What is Translation in Math? - Definition, Examples, & Terms 4:23
- Fixed Interval: Examples & Definition 4:00
- Scatterplot and Correlation: Definition, Example & Analysis 7:48
- Dilation in Math: Definition & Meaning 5:30
- Simplifying Fractions: Examples & Explanation 4:44
- Go to Overview of Math Concepts

- Communications 104: Intro to Mass Communications I
- Art 104: History of Western Art II
- Inclusion in Recruitment, Interviews & Hiring
- Computer Science 105: Introduction to Operating Systems
- High School 101: High School Readiness
- History & Culture of Mass Communication
- Mass Communication & Modern Society
- Introduction to Mass Communication
- Mass Communication & Book Publishing
- Models & Theories of Mass Communication
- List of FTCE Tests
- CLEP Prep Product Comparison
- CLEP Exam vs. AP Test: Difficulty & Differences
- CLEP Tests for the Military
- How to Transfer CLEP Credits
- CLEP Exam Question Formats
- CLEP Exam Costs & Registration Deadlines

- Robert Frost's Out, Out: Summary & Analysis
- The Monk in The Canterbury Tales: Description & Social Class
- Poe's A Dream Within a Dream: Summary, Theme & Analysis
- Good Country People: Summary, Characters, Theme & Analysis
- Dusky v. United States: Case, Summary & Facts
- Indian Art Lesson for Kids: History & Types
- Law of Reciprocal Proportion: Definition & Examples
- Types of Films: Examples & Product Placement
- Quiz & Worksheet - Ethics of Care & Justice Theory in Business
- Quiz & Worksheet - Organizational Core Values & Ethics
- Understanding Swamps: Quiz & Worksheet for Kids
- Quiz & Worksheet - Characterization in The Canterbury Tales
- Quiz & Worksheet - Change in Organization & Resource Dependency
- How to Cite Sources Flashcards
- Evaluating Sources for Research Flashcards

- Remedial Algebra I
- McDougal Littell The Americans: Online Textbook Help
- Intro to PowerPoint: Essential Training & Tutorials
- AP Calculus AB & BC: Homeschool Curriculum
- Algebra II: High School
- Kinematics Principles: Help and Review
- Linear Momentum in Physics: Help and Review
- Quiz & Worksheet - Components of Environmental Planning & Decision Making
- Quiz & Worksheet - Elastic Demand
- Quiz & Worksheet - Electrical Resistance
- Quiz & Worksheet - SEO Definition & Examples
- Quiz & Worksheet - Impact of Geographic Segmentation in Marketing

- What is Project Procurement Management? - Definition & Process
- Area Method: Slope & Examples
- Praxis Tests in Pennsylvania
- Praxis Tests in Idaho
- Romeo and Juliet Project Ideas
- How to Earn a Micro Credential
- How Hard is it to Learn French?
- Common Core State Standards in New Mexico
- 504 Plans in Georgia
- 504 Plans in Colorado
- Fun Math Games for 4th Grade
- 3rd Grade Word Walls

Browse by subject