What does a negative exponent mean?

A negative exponent means 'take the reciprocal.' For example, 2⁻³ = 1/2³ = 1/8 = 0.125. The base is raised to the positive exponent, then flipped to a fraction.

What does a fractional exponent mean?

A fractional exponent combines powers and roots. a^(m/n) means the nth root of a raised to the m power. For example, 8^(1/3) = ∛8 = 2, and 8^(2/3) = (∛8)² = 4.

Can I raise a negative number to a fractional power?

Negative bases with fractional exponents can produce complex (imaginary) numbers. For example, (-1)^(1/2) = √(-1) = i. This calculator only handles real number results.

What are the most common exponent rules?

The key rules are: aᵐ × aⁿ = aᵐ⁺ⁿ (product rule), aᵐ/aⁿ = aᵐ⁻ⁿ (quotient rule), (aᵐ)ⁿ = aᵐⁿ (power rule), a⁰ = 1, and a⁻ⁿ = 1/aⁿ.

general

Exponent Calculator

Calculate any base raised to any exponent. Supports negative, fractional, and zero exponents with step-by-step rules shown.

Last updated: March 31, 2026

Base

Exponent

How to Use This Calculator

Enter the base number (any real number, including negatives and decimals).
Enter the exponent (supports integers, fractions, and negatives).
Click Calculate to see the result with rules and step-by-step breakdown.

The Formula

aⁿ = a × a × ... × a (n times). Special rules: a⁰ = 1 (a ≠ 0), a¹ = a, a⁻ⁿ = 1/aⁿ, a^(1/n) = ⁿ√a.

Frequently Asked Questions

0⁰ is mathematically undefined (indeterminate). Different mathematical contexts assign it different values — in combinatorics it is treated as 1, but in analysis it is left undefined. This calculator treats it as undefined.