# Formulas and properties of exponents.

Definition

When n is a positive integer, the number c is called the n power of the number a if
c = a^{n} = |
a · a · ... · a |

n |

**Formulas and properties of exponents** are used in the reduction and simplification of expressions, and in solving equations and inequalities.

1. | a^{0} = 1 (a ≠ 0) | - zero exponent property |

2. | a^{1} = a | - any number raised by the exponent 1 is the number itself |

3. | a^{n} · a^{m} = a^{n +
m} | - product of powers property |

4. | (a^{n})^{m} = a^{nm} | - power of a power property |

5. | a^{n}b^{n} = (ab)^{n} | - power of a product property |

6. | a^{-n} = ^{n} | - negative exponent property |

7. | ^{n}^{m}^{n - m}
| - quotient of powers property |

8. | a^{1/n} = ^{n}√a | - rational exponent property |

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