# Zero Exponents

An exponential number is a function that is expressed in the form of ${x}^{n}$ , where x represents a constant, known as the base; and n, the exponent of the function, can be any number. The exponent defines how many times the base is multiplied by itself. For example, ${3}^{4}$ represents the operation $3\times 3\times 3\times 3=81$ .

Many students find it strange that anything raised to the power of 0 is 1. A lot of students think it should be 0, just like anything multiplied by 0 is 0. But remember, you are not multiplying by the exponent, but using the exponent to tell how many times to multiply a number by itself.

## Using the product of powers property to see how zero exponents work

We can use the product of powers property to see exactly how the 0 exponent works.

${9}^{0}\times {9}^{1}={9}^{(0+1)}={9}^{1}$

We already know that ${9}^{1}=9$ . The product of powers property says that ${9}^{0}\times 9=9$ . If we try to multiply $0\times 9$ , we get 0, so ${9}^{0}$ can't equal 0. We do know that $1\times 9=9$ , so ${9}^{0}$ has to equal 1.

The general rule is that for all real numbers x where $x\ne 0$ , we have:

${x}^{0}=1$

## Using the quotient of powers property to show how zero exponents work

We can also use the quotient of powers property to show that a number with a 0 exponent equals 1.

We know that $\frac{{x}^{2}}{{x}^{2}}=1$ using the quotient of powers property because when we divide numbers with the same base, we subtract the exponents.

That means that $\frac{{x}^{2}}{{x}^{2}}={x}^{(2-2)}={x}^{0}$ , and we already know that $\frac{{x}^{2}}{{x}^{2}}=1$ , so we can see that ${x}^{0}=1$ . That is, any number (except 0) raised to the power of 0 equals 1.

Note that ${0}^{0}$ is undefined.

## Topics related to the Zero Exponents

## Flashcards covering the Zero Exponents

Common Core: 6th Grade Math Flashcards

## Practice tests covering the Zero Exponents

MAP 6th Grade Math Practice Tests

## Get help learning about zero exponents

Tutoring is an excellent way for your student to gain a more thorough understanding of zero exponents. Face it, zero exponents can be a little bit tricky. They are not intuitive. If your student could use some help with them, a tutor is just the right choice. A tutor can meet with your student in 1-on-1 sessions using customized learning materials that focus on their most effective way of learning. A tutor can also try multiple ways of looking at zero exponents until they find one that works well for your student. To get connected with an expert tutor who can help your student understand zero exponents and more math topics, contact the Educational Directors at Varsity Tutors today.

- PHR - Professional in Human Resources Training
- TEFL - Teaching English as a Foreign Language Training
- Eleven Plus Exam Tutors
- CFA Courses & Classes
- Stoichiometry Tutors
- East Asian Studies Tutors
- CCNA Wireless - Cisco Certified Network Associate-Wireless Test Prep
- STAAR Courses & Classes
- API - Associate in Personal Insurance Test Prep
- Series 24 Courses & Classes
- Michigan Bar Exam Test Prep
- PCAT Courses & Classes
- SAT Writing and Language Test Prep
- Medicine Tutors
- Real Analysis Tutors
- ARDMS - American Registry for Diagnostic Medical Sonography Test Prep
- StatCrunch Tutors
- Project Management Tutors
- Exam P - Probability Test Prep
- MCSD - Microsoft Certified Solutions Developer Test Prep

- French Tutors in New York City
- ISEE Tutors in Boston
- Chemistry Tutors in Phoenix
- English Tutors in Atlanta
- Statistics Tutors in San Francisco-Bay Area
- Algebra Tutors in Seattle
- French Tutors in San Francisco-Bay Area
- Computer Science Tutors in Dallas Fort Worth
- GMAT Tutors in Dallas Fort Worth
- Chemistry Tutors in Philadelphia