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Math Help - Powers - please help!

  1. #1
    Member princess_anna57's Avatar
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    Talking Powers - please help!

    Please help me calculate the following:

    16^(-1/2)
    (27)^(1/3) - with questions that have two brackets, only the first number has brackets on paper.
    (27)^(-1/3)
    (-27)^(1/3)
    (-27)^(-1/3)
    (-2)^(-3)
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  2. #2
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    Quote Originally Posted by princess_anna57 View Post
    Please help me calculate the following:

    16^(-1/2)
    (27)^(1/3) - with questions that have two brackets, only the first number has brackets on paper.
    (27)^(-1/3)
    (-27)^(1/3)
    (-27)^(-1/3)
    (-2)^(-3)
    x^{m/n} = \sqrt[n]{x^m}

    x^{-n} = \frac1{x^n}
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  3. #3
    Member princess_anna57's Avatar
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    Thanks!

    I got the first three, but I'm not sure about the last ones. What difference does it make if x is a negative? does it mean that it's undefined/does not exist?
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    Quote Originally Posted by princess_anna57 View Post
    I got the first three, but I'm not sure about the last ones. What difference does it make if x is a negative? does it mean that it's undefined/does not exist?
    Well, if you try to take the square root (or any even root) of a negative number, you will not get a real answer (because the square of any real number is nonnegative). However, you can take cube roots of a negative number, and in fact you can take the n^{\rm th} root of a negative number as long as n is odd.

    Thus, \sqrt[3]{-27} = -3, for example, because (-3)^3 = (-3)(-3)(-3) = -27.
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