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    Question

    What value should come in place of the question-mark (?) in the following questions:

    (〖(0.5)〗^(1/3)  × 〖(1/125)〗^(1/4)  ×

    〖25〗^(1/6)  ×〖(6.25)〗^(2/3))/(〖(2.5)〗^(2/3)  × 5^(-1/2)  × 〖(1/5)〗^(-2)×〖3125〗^((-1)/4) ) =?
    A 2/5 Correct Answer Incorrect Answer
    B 1/2 Correct Answer Incorrect Answer
    C 3/10 Correct Answer Incorrect Answer
    D 2/15 Correct Answer Incorrect Answer
    E 1/5 Correct Answer Incorrect Answer

    Solution

    (〖(0.5)〗^(1/3)  × 〖(1/125)〗^(1/4)  × 〖25〗^(1/6)  ×〖(6.25)〗^(2/3))/(〖(2.5)〗^(2/3)  × 5^(-1/2)  × 〖(1/5)〗^(-2)×〖3125〗^((-1)/4) )  = (5^(1/3)/〖10〗^(1/3)   × 1/5^(3/4)   × 5^(1/3)  × 5^(8/3)/〖10〗^(4/3) )/(5^(4/3)/〖10〗^(2/3)   × 5^(-1/2)  × 5^2  × 5^(-5/4) )  = (5^(1/3-3/4+1/3+8/3)   ×〖10〗^(-1/3-4/3))/(5^(4/3-1/2+2-5/4)  × 〖10〗^(-2/3) ) =  (5^(31/12)  × 〖10〗^(-5/3))/(5^(19/12)  × 〖10〗^(-2/3) ) = 5^(12/12)  × 〖10〗^(-1) = 1/2

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