What is a negative exponent?

A negative exponent represents the reciprocal of the base raised to the positive version of the exponent. For example, 2⁻³ = 1/2³ = 1/8 = 0.125. Negative exponents are commonly used in scientific notation to represent very small numbers.

What does a fractional exponent mean?

A fractional exponent represents a root. Specifically, x^(1/n) is the nth root of x. For example, 8^(1/3) = ∛8 = 2. And x^(m/n) = (nth root of x)^m. This unifies the concepts of powers and roots into a single generalised notation.

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Exponents & Powers Explained

How Exponentiation Works

An exponent (or power) indicates how many times a base number is multiplied by itself. 2⁴ = 2 × 2 × 2 × 2 = 16. The expression bⁿ means "b multiplied by itself n times."

Negative & Fractional Exponents

Negative Exponent: b⁻ⁿ = 1 / bⁿ. For example, 2⁻³ = 1/8 = 0.125.
Fractional Exponent: b^(1/n) is the nth root of b. b^(m/n) = (nth root of b)^m.
Zero Exponent: Any non-zero base raised to the power of 0 equals 1.

Scientific Notation

Exponents power scientific notation: expressing very large or very small numbers as a coefficient × 10ⁿ. Our calculator displays results in scientific notation automatically when the output exceeds six digits.