## Laws of Indices

To multiply numbers with the same base, keep the base and add the indices. | |

To divide numbers with the same base, keep the base and subtract the indices. | |

When raising a power to a power, keep the base and multiply the indices. | |

The power of a product is the product of the powers. | |

A power of a quotient is the quotient of the powers. | |

The root of a quotient is the quotient of the roots . | |

The root of a quotient raised to a power is the quotient of the roots of the powers. | |

(is not defined) | Any non-zero number raised to the power of zero is 1. |

and | A negative exponent means take the reciprocal. |

A root is a fractional power. Taking the nth root is the same as raising to the power | |

Using the third and seventh rules allows us to raise a root to a power. |