`a, ( 5/12 + 1/3 )^2 + ( 3/4 - 5/6 )^2`
`= (3/4)^2 + (-1/12)^2 `
`= (3^2)/(4^2) + (-1^2)/(12^2)`
`= 9/16 + 1/144 = 41/72`
`b, (3^2)^2 - [ (-5)^2^1 + [(-2)^3]^2`
`= 3^4 + 5^2 + (-2)^6`
`= 81 + 25 + 64 = 106 + 64 `
`= 170`
`c, 4 × (1/4)^2 + 25 × [(3/4)^3 : (5/4)^3)] : (3/2)^3`
`= 4 × (1^2)/(4^2) + 25 × [(3^3/(4^3) × (4^3)/(5^3)] × (2^3)/(3^3) `
`= 4 × 1/16 + 25 × [ 27/64 × 64/125 ] × 8/27`
`= 1/4 + 25 × 27/125 × 8/27 = 1/4 + 27/5 × 8/27 `
`= 1/4 + 8/5 = 37/20`
`d, 2^3 + 3 × (1/2)^0 - 1 + [ (-2)^2 : 1/2 ] - 8 `
`= 8 + 3 × 1 - 1 + [ 4 × 2 ] - 8 `
`= 8 + 3 - 1 + 8 - 8`
`=10`