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    Question

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

    (〖(0.4)〗^(1/3)  × 〖(1/64)〗^(1/4)  ×

    〖16〗^(1/6)  × 〖(0.256)〗^(2/3))/(〖(0.16)〗^(2/3)  × 4^(-1/2)  ×〖1024〗^(-1/4) ) = ?
    A 4/5 Correct Answer Incorrect Answer
    B 2/5 Correct Answer Incorrect Answer
    C 7/5 Correct Answer Incorrect Answer
    D 3/5 Correct Answer Incorrect Answer
    E 3/10 Correct Answer Incorrect Answer

    Solution

    ⇒ (〖(0.4)〗^(1/3)  × 〖(1/64)〗^(1/4)  × 〖16〗^(1/6)  × 〖(0.256)〗^(2/3))/(〖(0.16)〗^(2/3)  × 4^(-1/2)  ×〖1024〗^(-1/4) )  ⇒ (4^(1/3)/〖10〗^(1/3)   × 1/4^(3/4)   × 4^(1/3)  × 4^(8/3)/〖10〗^(4/3) )/(4^(4/3)/〖10〗^(2/3)   × 4^(-1/2)  × 4^2  × 4^(-5/4) )    ⇒ (4^(1/3)×〖10〗^(-1/3)× 4^(-3/4)×4^(1/3)×4^(8/3)×〖10〗^((-4)/3))/(4^(4/3)  × 〖10〗^(-2/3)× 4^(-1/2)  × 4^2  × 4^(-5/4)  ) ⇒ (4^(1/3- 3/4+ 1/3+ 8/3)  × 〖10〗^(-1/3-4/3))/(4^(4/3-1/2+ 2-5/4)  × 〖10〗^(-2/3) ) ⇒ (4^(31/12)  × 〖10〗^(-5/3))/(4^(19/12)  × 〖10〗^(-2/3) ) ⇒ 4^(31/12- 19/12)  × 〖10〗^(-5/3+ 2/3) ⇒ 4^(12/12)  ×  〖10〗^(-1) ⇒ 4/10 ⇒ 2/5

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