Exponent calculator
Raise any number to any power: whole, negative, decimal or fraction (type 2/3). Results in full and in scientific notation.
Exponent rules
| Rule | Formula | Example |
|---|---|---|
| Product | aᵐ · aⁿ = aᵐ⁺ⁿ | 2³ · 2⁴ = 2⁷ = 128 |
| Quotient | aᵐ / aⁿ = aᵐ⁻ⁿ | 5⁶ / 5⁴ = 5² = 25 |
| Power of a power | (aᵐ)ⁿ = aᵐⁿ | (3²)³ = 3⁶ = 729 |
| Zero exponent | a⁰ = 1 (a ≠ 0) | 7⁰ = 1 |
| Negative exponent | a⁻ⁿ = 1/aⁿ | 2⁻³ = 1/8 |
| Fractional exponent | a^(m/n) = ⁿ√(aᵐ) | 8^(2/3) = 4 |
| Power of a product | (ab)ⁿ = aⁿbⁿ | (2·5)³ = 1000 |
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Evaluate (2)^(10) = 1,024
Questions people ask
What does a negative exponent mean?
It means “one over”: a⁻ⁿ = 1/aⁿ. So 10⁻³ = 1/1000 = 0.001. The minus sign flips the number to the other side of a fraction bar; it never makes the result negative.
What does a fractional exponent mean?
The denominator is a root and the numerator a power: 27^(2/3) = (∛27)² = 3² = 9.
Why is anything to the power 0 equal to 1?
Follow the quotient rule: aⁿ / aⁿ = aⁿ⁻ⁿ = a⁰, and any non-zero number divided by itself is 1. 0⁰ is left undefined in some contexts; this calculator follows the common computing convention 0⁰ = 1.
Is −2² equal to 4 or −4?
−4. The exponent applies before the minus sign. Enter (−2) as the base to get 4, which is what this calculator does because the base is always bracketed.