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# Module 12

### Module 12: Rational Exponents

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

Write the expression in radical form 6^(3/2) | The denominator of 2 becomes the index. The numerator of 3 becomes the power which it is raised by. (√6)^3 Square root of 6 to the third power. |

Write the expression in radical form 7^(4/3) | The denominator of 3 becomes the index. The numerator of 4 becomes the power by which its raised. (3√7)^4 Cube root of 7 raised to the 4th power |

Write the expression in exponential form (√10)^3 Square root of 10 cubed | The understood index of 2 becomes the denominator. The numerator is 3 because the that is the power its raised to. 10^(3/2) |

Write the expression in exponential form (3√6x)^4 Cube root of 6x raised to the fourth power | The index of 3 becomes the denominator. The numerator is 4 because the that is the power its raised to. (6x)^(4/3) |

What is the Power Rule? | The Power Rule: (a^m)^n = a^mn |

What is the Product Rule? | The Product Rule: (a^m)*(a^n) = a^m+n |

What is the Quotient Rule? | The Quotient Rule: (a^m)/(a^n) = a^m-n |

Simplify (-64)^(2/3) | Rewrite as cubed root of negative 64 squared. (3√-64)^2. Cube root the negative 64 leaving -4. (-4)^2. Then square the -4, giving the answer of 16. |

Simplify (4√16x^2) Fourth root of 16x squared | Fourth root the 16 and pull out the 2. 2(4√x^2). Divide out the fourth root of x. 2x^(2/4). Simplify the 2/4 to 1/2. 2x^1/2. x^(1/2) is the square root of x. 2√x is the answer. |

Simplify 6√x^3 Sixth root of x cubed | Divide out the index into the x cubed. x^(3/6). Simplify. x^(1/2). x^(1/2) = √x. The answer is √x. |