# Exponent Calculator — Powers, Roots & Negative Exponents

> Compute base to any power: positive, negative or fractional exponents (roots), with scientific notation for very large or very small results. Free and instant.

- **Category:** Math
- **Interactive calculator:** https://youcalc.com/en/math/exponent-calculator/
- **Price:** Free, no sign-up required

## Overview

Raising a number to a power is repeated multiplication: the base is the number you start with and the exponent says how many times to multiply it by itself. This calculator evaluates base^exponent for any real base and any real exponent — whole numbers, negatives and fractions alike — so it doubles as a square-and-cube tool, a roots tool and a reciprocal tool. Type the two numbers and the result appears instantly, with scientific notation offered whenever the answer is very large or very small.

## How to read your result

The big figure is the value of base^exponent. Below it you can read the same number in scientific notation (for example 1e+12 means 1 followed by twelve zeros), which is easier to scan once a result runs past a billion or drops below a ten-thousandth. If you raise a negative base to a fraction — say (−2)^0.5 — the calculator shows "No real result" instead of a number, because that power has no value among the real numbers; switch to a whole-number exponent or a positive base to get an answer.

## Method

For a positive whole-number exponent n, base^n multiplies the base by itself n times, and base^0 = 1 for any base. A negative exponent is the reciprocal of the positive power: base^(−n) = 1 ÷ base^n. A fractional exponent is a root: base^(1/n) is the n-th root of the base, and base^(p/q) is the q-th root of base raised to the p-th power. A negative base only stays real when the exponent is a whole number or a fraction whose reduced denominator is odd (so (−8)^(1/3) = −2 is fine, but (−2)^0.5 is not). All input is validated as a finite real number before the power is evaluated.

## Example

- **Setup:** Base 2, exponent 10.
- **Result:** 2^10 = 1024, because 2 is multiplied by itself ten times. Flip the exponent to −2 and you get 2^−2 = 1 ÷ 2² = 0.25 (the reciprocal of the square). Use a fractional exponent and 27^(1/3) = 3, the cube root of 27.

## Frequently asked questions

### What does a negative exponent mean?

A negative exponent is the reciprocal of the positive power. b^(−n) equals 1 ÷ b^n, so 5^−2 = 1 ÷ 5² = 1 ÷ 25 = 0.04. The base never becomes negative just because the exponent is negative — it simply moves to the denominator.

### How does a fractional exponent work?

A fractional exponent is a root. b^(1/n) is the n-th root of b, so 27^(1/3) = 3 (the cube root of 27) and 2^0.5 = √2 ≈ 1.4142. More generally b^(p/q) is the q-th root of b, raised to the power p.

### Why does (−2)^0.5 say "No real result"?

Taking an even root of a negative number has no real answer — there is no real number that squares to −2. Such powers exist only in the complex numbers. A negative base raised to a fraction is real only when the reduced denominator is odd, like (−8)^(1/3) = −2.

### Is 0^0 equal to 1?

This calculator returns 0^0 = 1, following the common combinatorial convention also used by most programming languages and spreadsheets. The expression is sometimes called indeterminate in the context of limits, but as a discrete power it is taken to be 1 here.

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- [Compound Interest Calculator](https://youcalc.com/en/finance-money/compound-interest/)

## Sources

- https://mathworld.wolfram.com/Power.html
- https://en.wikipedia.org/wiki/Exponentiation

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Interactive version: https://youcalc.com/en/math/exponent-calculator/ · From YouCalc — https://youcalc.com