The **exponent** that a number says **how plenty of times** to usage the number in a multiplication.

You are watching: 2 to the power of -1

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

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

Exponents are likewise called powers or Indices.

Some more examples:

### Example: **53 = 5 × 5 × 5 = 125**

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

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

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

## Another means of composing It

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

## Negative Exponents

Negative? What could be opposing of multiplying? Dividing!

So we division by the number every time, i m sorry is the exact same as multiplying by *1***number**

## Negative? flip the Positive!

That last example showed one easier means to handle an adverse exponents: calculation the hopeful exponent (an) |

More Examples:

negative 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 itself (example 91 = 9) | |

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

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

## It All makes Sense

If you look at the table, friend will see that positive, zero ornegative exponents room really component of the exact same (fairly simple) pattern:

Example: strength of 5

.. Etc.. See more: The Battle Of English And Mathematics Answer, The Battle Of English Vs | |||

52 | 5 × 5 | 25 | |

51 | 5 | 5 | |

50 | 1 | 1 | |

5-1 | 15 | 0.2 | |

5-2 | 15 × 15 | 0.04 | |

.. Etc.. |