The **exponent** of a number states **how plenty of times** to use the number in a multiplication.

You are watching: 6 to the power of 5

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

In words: 82 might be referred to as "8 come the strength 2" or "8 come the second power", or just "8 squared"

Exponents are also called strength or Indices.

Some more examples:

### Example: **53 = 5 × 5 × 5 = 125**

In words: 53 can be referred to as "5 to the 3rd power", "5 to the strength 3" or just "5 cubed" ### Example: **24 = 2 × 2 × 2 × 2 = 16**

In words: 24 could be referred to as "2 to the 4th power" or "2 come the strength 4" or simply "2 come the 4th" So** in general**:

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

## Another means of creating It

Sometimes world use the **^** price (above the 6 on your keyboard), as it is straightforward to type.

## Negative Exponents

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

So we division by the number each time, i beg your pardon is the exact same as multiply by *1***number**

## Negative? upper and lower reversal the Positive!

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

More Examples:

an unfavorable Exponent mutual of

**Positive Exponent price**

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, climate you just have actually the number chin (example 91 = 9) | |

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

But what about 00 ? It could be one of two people 1 or 0, and also so world say it is "indeterminate". |

## It All renders Sense

If girlfriend look at that table, you will check out that positive, zero ornegative exponents space really part of the exact same (fairly simple) pattern:

Example: powers of 5

.. Etc.. See more: What Distinguishes A Heart Attack From Heart Failure & Arrest | |||

52 | 5 × 5 | 25 | |

51 | 5 | 5 | |

50 | 1 | 1 | |

5-1 | 15 | 0.2 | |

5-2 | 15 × 15 | 0.04 | |

.. Etc.. |