Positive, Zero and Negative Exponents

Videos, worksheets, stories and songs to help Grade 6 students learn how to evaluate positive, zero and negative exponents.

For example,
3² = 9, 3⁰ = 1, 3^-1= 1/3

There is also an explanation why a^-b = 1/a^b and why a⁰ =1
If the exponent is 0 then the answer is always 1. 
For example, 8⁰ = 1, 17⁰ = 1
Some mathematicians define 0⁰ = 1, whereas others leave it undefined

Positive and Negative Exponents
Positive exponents are easy, but what happens when you have zero for the exponent? Or even worse, a negative number?

Pattern for zero and negative exponents
Example:
5³ = 5 • 5 • 5
5² = 5 • 5
5¹ = 5
5⁰ = 1
5^-1 = 1/5
5^-2 = 1/5²
5^-3 = 1/5³

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Zero and negative exponent properties
Zero Exponent Property
Any quantity raised to the zero power equals 1.

Negative Exponent Property
a^-n = the reciprocal of aⁿ
a^-n = 1/aⁿ

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Definitions, covers negative exponents and zero as an exponent

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Negative Exponent Intuition
Intuition on why a^-b = 1/a^b (and why a⁰ = 1)

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Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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