Why is anything to the power zero equal to one?

Because dividing a power by itself gives one, and the exponent rule turns that division into a subtraction that lands on zero. It is a consequence of the rules rather than a separate convention.

What is zero to the power zero?

It depends on who you ask. Combinatorics takes it as one because it counts the empty product; analysis often leaves it undefined because the limit depends on the path. This declines rather than pick a side.

Math & Statisticsalgebra

Exponent Calculator

A base raised to any power, including negative and fractional exponents, with the result in scientific notation when it runs long. A negative exponent is a reciprocal, not a negative number.

Also called: power calculator, exponentiation.

Result

1,024

2 to the power 10 is 1,024. The base multiplied by itself that many times.

The reciprocal power

In scientific notation

1.024 x 10^3

Digits before the decimal point

Worth knowing

The base multiplied by itself that many times.

How this is calculated

Method and background

How this is calculated

Multiplying the base by itself as many times as the exponent says, extended to cases where that description stops working. A negative exponent inverts: two to the minus three is one eighth, not minus eight. A fractional exponent is a root: nine to the power one half is three. A zero exponent is one for every base except zero itself, where the expression has no agreed value.

result = base ^ exponent

b: The base
n: The exponent

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

two to the tenth

Base: 2
Exponent: 10

Result1,024

arithmetic identity

Open this example

a negative exponent is a reciprocal

Base: 2
Exponent: -3

Result0.13

boundary: the most misunderstood case in the whole tool

Open this example

Method and limits

What it assumes

A real base and a real exponent.

What it deliberately does not model

A negative base with a fractional exponent has no real value, and that returns nothing rather than a NaN.
Results beyond about 1e308 exceed what a double can hold and are reported as not finite.

Formula version 1.0.0 · definition 1.0.0 · United States · Report a problem with this calculator

Frequently asked questions

Why is anything to the power zero equal to one?: Because dividing a power by itself gives one, and the exponent rule turns that division into a subtraction that lands on zero. It is a consequence of the rules rather than a separate convention.
What is zero to the power zero?: It depends on who you ask. Combinatorics takes it as one because it counts the empty product; analysis often leaves it undefined because the limit depends on the path. This declines rather than pick a side.