# Base (exponentiation)

Calculation results | |
---|---|

Addition (+) | |

Subtraction (−) | |

Multiplication (×) | |

Division (÷) | |

Modulo (mod) | |

Exponentiation | |

nth root (√) | |

Logarithm (log) | |

In exponentiation, the **base** is the number `b` in an expression of the form `b ^{n}`.

## Related terms

The number `n` is called the exponent and the expression is known formally as exponentiation of `b` by `n` or the exponential of `n` with base `b`. It is more commonly expressed as "the `n`th power of `b`", "`b` to the `n`th power" or "`b` to the power `n`". For example, the fourth power of 10 is 10,000 because 10^{4} = 10 × 10 × 10 × 10 = 10,000. The term *power* strictly refers to the entire expression, but is sometimes used to refer to the exponent.

## Roots

When the `n`th power of `b` equals a number `a`, or `a` = `b ^{n}`, then

`b`is called an "

`n`th root" of

`a`. For example, 10 is a fourth root of 10,000.

## Logarithms

The inverse function to exponentiation with base `b` (when it is well-defined) is called the logarithm to base `b`, denoted log_{b}. Thus:

- log
_{b}*a*=*n*.

For example, log_{10} 10,000 = 4.