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    xMerlina's Avatar
    xMerlina Posts: 38, Reputation: 1
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    #1

    Mar 22, 2012, 07:18 PM
    Rewrite a fractional exponent as a radical?
    I'll just ask a portion of the question:

    How does the fractional exponent in (3/7)9^(7/3) simplify to 384/7 and how does (3/4)9^1/3 simplify to [I don't know the answer to this... it's either 12, 3/7, or 3/4]?

    I'd understand it if the exponent was a square root, but with a cube root, I'm lost.
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #2

    Mar 23, 2012, 08:51 AM
    does not equal .

    And:



    does not equal any of the possible answers you gave. Note that the cube root of 9 is an irrational number, so the answer can't be a simple fraction.
    xMerlina's Avatar
    xMerlina Posts: 38, Reputation: 1
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    #3

    Mar 23, 2012, 02:38 PM
    I'm confused now... my teacher and my textbook claim it's possible O_O

    http://college.cengage.com/mathematics/blackboard/content/larson/calc8e/04/04e/se04e01087.html
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #4

    Mar 24, 2012, 07:58 PM
    I think I figured it out. You mis-wrote the equations - instead of 9 being taken to the power of 7/3 it should be 8 to the 7/3.

    8^(7/3) = 8^((1/3) ^7)

    8^(1/3) =2, and 2^7 = 128. Do you see why 8^(1/3) is 2?

    3/7 x 128 = 384/7.

    As for the second problem, you have (3/4)8^(1/3). From what I showed above can you complete this?
    xMerlina's Avatar
    xMerlina Posts: 38, Reputation: 1
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    #5

    Mar 25, 2012, 04:29 PM
    Oh, that was stupid. Thank you!
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