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-   -   Properties of rational exponents HELP (https://www.askmehelpdesk.com/showthread.php?t=7317)

  • Jan 22, 2005, 09:32 PM
    fairiean9el
    properties of rational exponents HELP
    Hi ! I want to know if I answered this math problem correctly: the directions are to simplify the expression and assume all variables are positive.

    Problem:
    ( 2 ^1/3 x 5 ^ 1/2 ) 4

    My work:

    ( 2 ^1/3 x 5 ^ 1/2 ) 4 =

    2 ^ 4/3 x 5 ^ 2 =

    2 ^ 4/3 x 25

    Thanks so much for helping!! =] :D
  • Jan 26, 2005, 06:01 AM
    reinsuranc
    I don't think you are treating that 4 correctly
    ( 2 ^1/3 x 5 ^ 1/2 ) 4

    I would like to rewrite and add some extra parentheses just to be clear:

    ( 2^(1/3) x 5^(1/2) ) x 4

    ( 2^(1/3) x 5^(1/2) x 2^2 )

    ( 2^(1/3) x 2^2 x 5^(1/2) )

    ( 2^(1/3 + 2) x 5^(1/2) ) ; this is because (y^a)times(y^b) = y^(a+b).

    ( 2^(7/3) x 5^(1/2) )

    This equals about 11.27

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