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# Rational Exponents

### Math113 online Course Project

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

Solve: 8^2/3 | The denominator of the rational exponent corresponds with the index of the radical. 3√8^2 = 3√64 = 4, or (3√8)^2 = 2^2 = 4 |

Solve: -16^3/4 | Answer: -(4√16)^3 = -(2)^3 = -8 |

Solve: (4x-1)^3/5 | Answer: 5√(4x-1)^3 |

Solve: 16^-3/4 | Answer: 1/16^3/4 = 1/(4√16)^3 = 1/2^3 = 1/9 |

Solve: 81^1/2 | The denominator of the rational exponent corresponds with the index of the radical. 2√81 is the same as √81. Answer: √81 = 9 |

Solve: (81x^8)^1/4 | Answer: 4√81x^8 = 3x^2 |

Use Rational Exponents to simplify: 8√x^4 | Answer: x^4/8 = x^1/2 = √x |

Define: a^1/n | If n is a positive number greater than 1 and n√a is a real number, then a^1/n = n√a |

Define: a^m/n | If m and n are positive integers greater than 1 with m/n in lowest terms then a^m/n = n√a^m = (n√a^)^m, as long as n√a is a real number |

Define: a^-m/n | As long as a^m/n is a nonzero real number, a^-m/n = 1/(a^m/n) |

Created by:
Bucelee