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Exponent Calculator
Raise a number to any power — positive, negative or fractional — and see the math behind the result.
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How to Use This Calculator
- 2¹⁰ — base 2, exponent 10 → 1,024.
- 2⁻² — base 2, exponent −2 → 1/4 = 0.25.
- 9^(1/2) — base 9, exponent 0.5 → 3 (the square root).
Frequently Asked Questions
What does a negative exponent mean?
It means the reciprocal: 2⁻³ = 1/2³ = 1/8. The result is always between 0 and 1 for positive bases.
What is a fractional exponent?
It combines a power and a root: b^(m/n) = ⁿ√(bᵐ). For example, 8^(2/3) = (³√8)² = 4.
What is any number to the power of 0?
Any non-zero base to the power 0 equals 1. 0⁰ is undefined in most contexts.
Can the base be negative?
Yes — negative bases work with integer exponents. Fractional exponents on negative bases can produce imaginary results, which this tool flags.
Practical Example
A few operations to try:
- 2¹⁰ → 1,024 (bits in a kilobyte, roughly)
- 2⁻² → 1/4 = 0.25 (negative exponent = reciprocal)
- 9^(1/2) → 3 (fractional exponent = root)
- 10⁶ → 1,000,000 (a million)
What Your Results Mean
- Positive exponent — repeated multiplication (bⁿ).
- Negative exponent — the reciprocal 1/bⁿ, always between 0 and 1 for positive bases.
- Fractional exponent — a root combined with a power (b^(m/n) = ⁿ√(bᵐ)).
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