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Math Help - Exact Value of Indices

  1. #1
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    Exact Value of Indices

    Is there a simple way to find the exact value of these? There are no examples in the textbook for indices, other than powers of 1/2 and 1/3.



    1. (1/36)^-3/2
    2. 216^1/6 x 216^1/6
    3. 9^3/2 x 7^1

    Thanks in advance.
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  2. #2
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    Quote Originally Posted by JadeKiara View Post
    Is there a simple way to find the exact value of these? There are no examples in the textbook for indices, other than powers of 1/2 and 1/3.



    1. (1/36)^-3/2
    2. 216^1/6 x 216^1/6
    3. 9^3/2 x 7^1

    Thanks in advance.
    \left(\frac{1}{36}\right)^{-\frac{3}{2}} = 36^{\frac{3}{2}} = \left(36^{\frac{1}{2}}\right)^3 = 6^3 = 216

    \left(216^{\frac{1}{6}}\right)^2 = 216^{\frac{1}{3}} = 6

    you do the last one ...
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  3. #3
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    hi
    \forall x\in \mathbb{R}^{+*},x^{\frac{1}{n}}=\exp(\frac{1}{n}\l  n x)
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  4. #4
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    9^3/2 x 7^1
    = (9^1/2)^3 x 7
    = 27 x 7
    = 189.
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  5. #5
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    Quote Originally Posted by JadeKiara View Post
    9^3/2 x 7^1
    = (9^1/2)^3 x 7
    = 27 x 7
    = 189.
    Good
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