# 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 |

Factoring: Some special cases
Formulas and properties of exponents
Formulas and properties of nth root
Formulas and properties of logarithms
Formulas and properties of arithmetic sequence
Formulas and properties of geometrical sequence
Trigonometry formulasDerivative formulas
Integrals table

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