The laws of exponents are explained here along with their examples.

If ‘x’ is a non-zero integer or a non-zero rational number.

Laws | Rule | Example |

Product Rule | Keep base, + exponents (x ^{a}) (x^{b}) = x^{(a+b)} | |

Quotient rule | Keep base, – exponents (x ^{a}) ÷ (x^{b}) = x^{(a-b)} | |

Power of a power | Keep base, x exponents (x ^{a})^{b} = x^{(ab)} | |

Power of a product | Distribute exponents (xyz) ^{a} = x^{a}y^{a}z^{a} | |

Power of a quotient | Distribute exponents (x / y) ^{a} = x^{a }/y^{a} | |

Zero exponent | Any base with exponent 0 is equal to 1 (x) ^{0} = 1 | |

Negative exponent | Negative exponent can be rewritten with its reciprocal (x) ^{-a} = 1 / x^{a} |