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