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# c h a p t e r 7

### Powers

Question | Answer |
---|---|

Product of Powers Postulate | For any nonnegative bases and nonzero real exponents, or any nonzero bases and integer exponents, b^m x b^n = b^m+n |

Power of a Power Postulate | For any nonnegative bases and nonzero real exponents, or any nonzero bases and integer exponents, (b^m)^n = b^m x n |

Power of a Product Postulate | For any nonnegative bases and nonzero real exponents, or any nonzero bases and integer exponents, (ab)^m = a^m b^m |

Quotient of Powers Postulate | (b^m)/(b^n) = b^m-n |

Power of a Quotient Postulate | (a/b)^m = (a^m)/(b^m) |

Zero Exponent Theorem | if b is a nonzero real number, b^0 = 1 |

Negative Exponent Theorem | For any positive base b and real exponent n, or any nonzero base b and integer exponent n, b^-n = 1/(b^n) |

Annual Compound Interest Formula | A = P(1 + r)^t when P is the amount of money invested at an annual interest rate of r compounded annually. Let A be the total amount after t years. |

General Compound Interest Formula | Let P be the amount invested at an annual interest rate r compounded n times per year. Let A be the amount after t years. Then A = P(1 + (r/n))^nt |

Explicit Formula for a Geometric Sequence | In the geometric sequence with first term g*q and constant ratio r, g*n = g*1(r)^n-1 |

Number of Real Roots Theorem | Every positive real number has: 2 real nth roots, when n is even. 1 real nth root, when n is odd. Every negative real number has: 0 real nth roots, when n is even. 1 real nth root when n is odd. |

Created by:
katelesperance