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# Chapter 7

### Powers

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

Powering | x^n |

Base | the variable, x for example |

Exponent | the power, n for example |

Identity Function | x^1 |

2nd Power, Squaring | x^2 |

Cubing | x^3 |

Product of Powers | b^m x b^n = b^m+n |

Power of a Power | (b^m)^n = b^mXn |

Power of a Product | (ab)^m = a^m x b^m |

Quotient of Powers | b^m/b^n = b^m-n |

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

Zero Exponent | b^0 = 1 |

Negative Exponent | b^-n = 1/b^n |

Compounding | interest earns interest each year |

Annual Compound Interest Formula | A=P(1+r)^t |

General Compound Interest Formula | A=P(1+t/n)^nt |

Constant Ratio | constant multiplier, r |

Explicit Formula for a Geometric Sequence | Gn=G1(r)^n-1 |

B is the nth root of x only if | b^n=x |

1/n Exponent Theorem | when x is greater than or equal to 0 and n is an integer greater than one, 1/x^n is an nth root of x |

Number of Real Roots | POSITIVE REAL NUMBERS: n is even = 2 real nth roots n is odd = 1 real nth root NEGATIVE REAL NUMBERS: n is even = 0 real nth roots n is odd = 1 real nth root |

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