The **exponent** the a number says **how countless times** to usage the number in a multiplication.

You are watching: -3 to the 4th power

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

In words: 82 can be referred to as "8 come the strength 2" or "8 come the 2nd power", or merely "8 squared"

Exponents are likewise called powers 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 power 3" or just "5 cubed" ### Example: **24 = 2 × 2 × 2 × 2 = 16**

In words: 24 might be referred to as "2 come the fourth power" or "2 to the power 4" or merely "2 come the 4th" So** in general**:

an tells you to main point a through itself,so there space n of those a"s: |

## Another method of writing It

Sometimes human being use the **^** price (above the 6 on her keyboard), as it is simple to type.

## Negative Exponents

Negative? What could be opposing of multiplying? Dividing!

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

## Negative? flip the Positive!

That last example showed one easier way to handle negative exponents: calculation the optimistic exponent (an) |

More Examples:

an adverse 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, then you just have actually the number chin (example 91 = 9) | |

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

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

## It All provides Sense

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

Example: strength of 5

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52 | 5 × 5 | 25 | |

51 | 5 | 5 | |

50 | 1 | 1 | |

5-1 | 15 | 0.2 | |

5-2 | 15 × 15 | 0.04 | |

.. Etc.. |