# Free online exponent calculator

> An exponent tells you how many times to multiply a base number by itself. This calculator handles any base and exponent, including roots (fractional exponents) and negative powers.

Calculate any base raised to any power, including negative exponents, fractional exponents for roots, and very large numbers shown in scientific notation.

**Interactive version:** https://onlinecalculator.me/math/exponent/
**Category:** Math

## How to use

1. Enter a **base** number.
2. Enter an **exponent** (can be negative or fractional).
3. Click **Calculate** or press Enter.
4. See the result and scientific notation.

## Formula

**b^n = b × b × b × … (n times)**

For non-integer exponents: **b^(p/q) = q-th root of b^p**

## Key rules

| Expression | Result |
|-----------|--------|
| b^0 | 1 (any non-zero b) |
| b^1 | b |
| b^(−n) | 1/b^n |
| b^(1/2) | √b (square root) |
| b^(1/3) | ∛b (cube root) |
| b^(m/n) | n-th root of b^m |

## Worked examples

| Expression | Result |
|-----------|--------|
| 2^10 | 1,024 |
| 10^6 | 1,000,000 |
| 9^0.5 | 3 |
| 2^(−3) | 0.125 |
| 10^20 | 1 × 10^20 |

## Frequently asked questions

### What is an exponent?

An exponent (or power) tells how many times to multiply the base by itself. For b^n, b is the base and n is the exponent. 2^3 = 2 × 2 × 2 = 8.

### What does a negative exponent mean?

A negative exponent means take the reciprocal: b^(−n) = 1/b^n. So 2^(−3) = 1/8 = 0.125.

### How do fractional exponents work?

A fractional exponent represents a root: b^(1/n) is the nth root of b. So 9^(1/2) = √9 = 3, and 27^(1/3) = ∛27 = 3.

### What is b^0?

Any non-zero number raised to the power of 0 equals 1. This is a fundamental rule — 5^0 = 1, 100^0 = 1.

### What happens with a negative base and fractional exponent?

A negative base with a fractional exponent produces a complex (imaginary) number — for example, (−4)^0.5 = √(−4), which is imaginary. The calculator returns an error in this case.

## Sources

- [Exponentiation (base raised to a power)](https://en.wikipedia.org/wiki/Exponentiation) — Wikipedia

## Related calculators

- [Scientific notation calculator](https://onlinecalculator.me/math/scientific/) — Convert numbers to and from scientific notation.
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- [Standard deviation calculator](https://onlinecalculator.me/math/standard-deviation/) — Calculate mean and standard deviation.
- [Factorial calculator](https://onlinecalculator.me/math/factorial/) — Calculate n! for any positive integer.

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