# Eight Rules of Exponents and Calculator

# Laws of Exponents | Golden Rules of Exponents

An online exponents rule

Law Name | Law | Example | Rule |
---|---|---|---|

One Rule | x^{1} = x |
9^{1} = 9 |
Any number raised to the power of "1" equals itself. |

Zero Rule | x^{0} = 1 |
7^{0} = 1 |
Any non-zero number raised to the power of zero equals 1 |

Negative Exponent | x^{-1} = 1/x |
4^{-1} = 1/4 |
Any non-zero number raised to a negative power equals its reciprocal raised to the opposite positive power. |

Product Rule | x^{m}x^{n} = x^{m+n} |
x^{2}x^{3} = x^{2+3} = x^{5} |
When multiplying 2 powers that have the same base, you can add the exponents. |

Quotient Rule | x^{m}/x^{n} = x^{m-n} |
x^{6}/x^{2} = x^{6-2} = x^{4} |
Divide 2 powers with the same base by subtracting the exponents |

Power Rule | (x^{m})^{n} = x^{mn} |
(x^{2})^{3} = x^{2×3} = x^{6} |
Multiply the exponents |

Tower Rule | a^{nm} |
2^{22} = 2^{4} = 16 |
Multiply the exponents from the top down. |

Fraction Rule | Sum can be rewritten using radicals.Denominator of the fraction becomes the index of the radical. |