# Exponent Calculator

> Calculate bⁿ for any base and exponent, including negative and fractional powers. Whole-number powers are exact to hundreds of digits.

Category: Mathematics · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/exponent-calculator

Raise a number to any power. Whole-number answers are calculated exactly, digit for digit, and very large or small results are also shown in scientific notation.

Also called: Power calculator, Indices calculator.

## Inputs
- Base (b) (default 2)
- Exponent (n) (default 10)

## Results
- bⁿ
- Scientific notation

## Formula

```
bⁿ = b × b × … × b (n times);  b⁻ⁿ = 1 ÷ bⁿ;  b^(1/k) = the kth root of b;  b⁰ = 1
```

Where:
- b: the base
- n: the exponent (power or index)

## Worked example
1. 2¹⁰ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2.
2. Doubling ten times: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024.

**Result:** 2 to the power of 10 is 1,024.

## What the result means

A negative exponent means a reciprocal (2⁻³ = 1/8), and a fractional exponent means a root (9^0.5 = √9 = 3).

## Assumptions and limits
- Answers are real numbers only.
- A negative base with a non-whole exponent, such as (−8)^0.5, has no real answer and is rejected. Cube roots of negatives need the exponent exactly 1/3, which a decimal cannot represent.
- Non-integer results are shown to 12 significant digits.

## Questions

### Why is any number to the power 0 equal to 1?

Each step down in power divides by the base: 2³ = 8, 2² = 4, 2¹ = 2, so 2⁰ = 2 ÷ 2 = 1. The same holds for every non-zero base.

### What is 0 to the power 0?

It is taken as 1 by convention in algebra and combinatorics, which is what this calculator shows; in calculus it is treated as an indeterminate form.

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Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/exponent-calculator