The **exponent** of a number says **how many times** to use the number in a multiplication.

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In **82** the "2" says to use 8 twice in a multiplication,**so 82 = 8 × 8 = 64**

In words: 82 could be called "8 to the power 2" or "8 to the second power", or simply "8 squared"

Exponents are also called Powers or Indices.

Some more examples:

### Example: **53 = 5 × 5 × 5 = 125**

In words: 53 could be called "5 to the third power", "5 to the power 3" or simply "5 cubed" ### Example: **24 = 2 × 2 × 2 × 2 = 16**

In words: 24 could be called "2 to the fourth power" or "2 to the power 4" or simply "2 to the 4th" So** in general**:

an tells you to multiply a by itself,so there are n of those a"s: |

## Another Way of Writing It

Sometimes people use the **^** symbol (above the 6 on your keyboard), as it is easy to type.

## Negative Exponents

Negative? What could be the opposite of multiplying? Dividing!

So we divide by the number each time, which is the same as multiplying by *1***number**

## Negative? Flip the Positive!

That last example showed an easier way to handle negative exponents: Calculate the positive exponent (an) |

More Examples:

Negative Exponenns Reciprocal of

**Positive Exponenns Answer**

4-2 | = | 1 / 42 | = | 1/16 = 0.0625 |

10-3 | = | 1 / 103 | = | 1/1,000 = 0.001 |

(-2)-3 | = | 1 / (-2)3 | = | 1/(-8) = -0.125 |

## What if the Exponent is 1, or 0?

1 | If the exponent is 1, then you just have the number itself (example 91 = 9) | |

0 | If the exponent is 0, then you get 1 (example 90 = 1) | |

But what about 00 ? It could be either 1 or 0, and so people say it is "indeterminate". |

## It All Makes Sense

If you look at that table, you will see that positive, zero ornegative exponents are really part of the same (fairly simple) pattern:

Example: Powers of 5

.. etc.. See more: How Much Does A Small House Weigh ? (9 Easy Examples) | |||

52 | 5 × 5 | 25 | |

51 | 5 | 5 | |

50 | 1 | 1 | |

5-1 | 15 | 0.2 | |

5-2 | 15 × 15 | 0.04 | |

.. etc.. |