# Properties of Exponents

Let a and b be real numbers, variables, or algebraic expressions, and let m and n be integers. (All denominators and bases are nonzero.)

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Property | Example |
---|---|

a^m * a^n = a^(m + n) | 3^2 * 3^4 = 3^(2 + 4) = 3^6 = 729 |

(a^m)/(a^n) = a^(m - n) | (x^7)/(x^4) = x^(7 - 4) = x^3 |

a^-n = 1/a^n = (1/a)^n | y^-4 = 1/y^4 = (1/y)^4 |

a^0 = 1, a /= 0 | (x^2 + 1)^0 = 1 |

(ab)^m = a^m * b^m | (5x)^3 = 5^3 * x^3 = 125x^3 |

(a^m)^n = a^(mn) | (y^3)^-4 = y^(3*-4) = y^-12 = 1/y^12 |

(a/b)^m = a^m/b^m | (2/x)^3 = (2^3)/(x^3) = 8/(x^3) |

|a^2| = |a|^2 = a^2 | |(-2)^2| = |-2|^2 = 2^2 = 4 |