Free exponent calculator
Calculate any base raised to any power — enter base and exponent to see the result, including negative and fractional exponents, updated live, as you type.
On this page10 sections
Uses Math.pow (IEEE 754 double precision).
Results are estimates. Consult a professional.
How the exponent calculator works
An exponent (or power) tells you how many times to multiply a base number by itself. Exponents appear in growth and decay, scientific notation, computer memory, and countless formulas across science and engineering.
Key rules: multiplying same-base powers adds exponents (bᵐ × bⁿ = b^(m+n)); dividing subtracts them (bᵐ / bⁿ = b^(m−n)); raising a power to a power multiplies them ((bᵐ)ⁿ = b^(mn)).
NIST Digital Library of Mathematical Functions — §1.2 Elementary AlgebraWorked example: positive, negative, and fractional exponents
Three common exponent types: a large positive power, a negative exponent, and a fractional (root) exponent.
Powers of 2 and powers of 10
Powers of 2 are fundamental to computing (bits, bytes, memory); powers of 10 underpin scientific notation and the metric system.
| Exponent (n) | 2ⁿ | 10ⁿ |
|---|---|---|
| 0 | 1 | 1 |
| 1 | 2 | 10 |
| 2 | 4 | 100 |
| 3 | 8 | 1,000 |
| 4 | 16 | 10,000 |
| 5 | 32 | 100,000 |
| 6 | 64 | 1,000,000 |
| 7 | 128 | 10,000,000 |
| 8 | 256 | 100,000,000 |
| 9 | 512 | 1,000,000,000 |
| 10 | 1,024 | 10,000,000,000 |
2¹⁰ = 1,024 ≈ 10³, which is why a kilobyte (1 KB) is 1,024 bytes, not exactly 1,000.
Tips for working with exponents
Exponent rules are short but easy to misapply. These reminders cover the most common mistakes.
- Any number to the power 0 is 1 — including 1⁰ = 1 and 100⁰ = 1; the only exception is 0⁰, which is mathematically indeterminate.
- Negative base with even exponent is positive — (−3)² = 9, not −9; but −3² = −(3²) = −9 because the exponent binds only to 3.
- Fractional exponents are roots — x^(1/2) = √x and x^(1/3) = ³√x; use this to rewrite root problems as power problems.
- Scientific notation uses powers of 10 — 3.2 × 10⁶ means 3,200,000; to convert, move the decimal point by the exponent's value.
- Exponents in compound-interest formulas — A = P(1 + r/n)^(nt); the exponent nt is the total number of compounding periods, not just years.
Accuracy and limitations
Integer exponents are computed exactly up to the limits of double-precision floating-point (~15 significant digits). For very large exponents (e.g., 2¹⁰⁰⁰), results switch to scientific notation and may lose lower-order digits. Fractional exponents are computed via logarithms internally (b^(m/n) = e^((m/n)·ln b)), introducing small rounding errors beyond 15 significant figures. Negative bases with non-integer exponents produce complex numbers and are out of scope for this calculator.
Key terms
About this calculator
Part of our math calculators suite — explore all calculators.