Ba(OH)₂ is a strong base, therefore completely ionises in the solution as follows
Ba(OH)₂ --> Ba²⁺ + 2OH⁻
1 mol of Ba(OH)₂ gives out 2 mol of OH⁻
therefore number of OH⁻ moles are twice the amount of Ba(OH)₂ moles in the solution
hence,
[OH⁻] = 2[Ba(OH)₂]
therefore hydroxide ion concentration = 2 x 1.37 x 10⁻⁵ M
[OH⁻] = 2.74 x 10⁻⁵ M
coefficient = 2.74
exponent = -5
