Zero and Negative Exponents; Scientific Notation

Algebra Foundation

Algebra 1

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Algebra 1 · Unit 7 · Topic 7.2

Zero and Negative Exponents; Scientific Notation

For a ≠ 0, a⁰ = 1 and a⁻ⁿ = 1/aⁿ for a positive integer n.

Definition and explanation

For a ≠ 0, a⁰ = 1 and a⁻ⁿ = 1/aⁿ for a positive integer n. Scientific notation writes a nonzero number as c × 10ⁿ with 1 ≤ |c| < 10 and integer n.

Worked example

The number 0.000072 is 7.2 × 10⁻⁵ because moving the decimal five places gives 7.2. Also, 2⁻³ = 1/2³ = 1/8, not −8.

Common mistake

A negative exponent means a reciprocal, not a negative value.

Key takeaway

For a ≠ 0, a⁰ = 1 and a⁻ⁿ = 1/aⁿ for a positive integer n.

Explain each step of the worked example, then check the units, signs, and conditions that apply.

Further reading

Topic coverage was checked against the openly available OpenStax Elementary Algebra 2e and Algebra and Trigonometry 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.