# Exponent Calculator

Enter the base and exponent to calculate the result below.

a^{x} = ?

## Results:

^{x}=

## On this page:

## How to Calculate an Exponent

An exponent is the number of times the base value should be multiplied by itself. To calculate a number raised to an exponent, multiply the number by itself for each value of the exponent.

So 5^{2} is the same as 5 × 5 and 5^{3} is the same as 5 × 5 × 5.

Calculating an exponent is also sometimes referred to as raising a number to the nth power.

**For example,** calculate the result of 8^{4}.

8^{4} = 8 × 8 × 8 × 8

8^{4} = 4,096

Thus, 8^{4}, or 8 to the 4th power, is equal to 8 times 8 times 8 times 8, which is equal to 4,096.

## How to Calculate a Negative Exponent

What do you do if the exponent is negative? For a negative exponent rather than multiplying the number by itself the number of times for the exponent, you divide the number by itself, starting with 1.

So 5^{-2} is the same as 1 ÷ 5 ÷ 5 and 5^{-3} is the same as 1 ÷5 ÷ 5 ÷ 5.

Negative exponents are often expressed as 1 over the base with a positive exponent.

5^{-2} = 1 / 5^{2}

**For example,** calculate the result of 8^{4}.

8^{-4} = 1 / 8^{4}

8^{-4} = 1 / 8 × 8 × 8 × 8

8^{-4} = 1 / 4,096

8^{-4} = 0.000244140625

Thus, 8^{-4} is equal to 0.000244140625.

## Special Exponent Rules

There are some special rules with exponents that are important to remember.

When the exponent is 1, the result of raising a base to the exponent will always be equal to the base.

a^{1} = a

When the exponent is 0, the result of raising a base to the exponent will always be equal to 1.

a^{0} = 1

When the exponent is 2 you can also say that the base value is squared. When the exponent is 3 you can say that the base value is cubed.

The calculator above will handle these special cases along with negative exponents to solve the answer.

## Exponent Table

Powers of Two | Powers of Three | Powers of Four | Powers of Five |
---|---|---|---|

2^{0} = 1 |
3^{0} = 1 |
4^{0} = 1 |
5^{0} = 1 |

2^{1} = 2 |
3^{1} = 3 |
4^{1} = 4 |
5^{1} = 5 |

2^{2} = 4 |
3^{2} = 9 |
4^{2} = 16 |
5^{2} = 25 |

2^{3} = 8 |
3^{3} = 27 |
4^{3} = 64 |
5^{3} = 125 |

2^{4} = 16 |
3^{4} = 81 |
4^{4} = 256 |
5^{4} = 625 |

2^{5} = 32 |
3^{5} = 243 |
4^{5} = 1024 |
5^{5} = 3125 |

2^{6} = 64 |
3^{6} = 729 |
4^{6} = 4096 |
5^{6} = 15625 |

2^{7} = 128 |
3^{7} = 2187 |
4^{7} = 16384 |
5^{7} = 78125 |

2^{8} = 256 |
3^{8} = 6561 |
4^{8} = 65536 |
5^{8} = 390625 |

2^{9} = 512 |
3^{9} = 19683 |
4^{9} = 262144 |
5^{9} = 1953125 |

2^{10} = 1024 |
3^{10} = 59049 |
4^{10} = 1048576 |
5^{10} = 9765625 |