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