Answer is: concentration of hydronium ions are 10⁻¹³ M.
Chemical dissociation of barium hydroxide in water:
Ba(OH)₂(aq) → Ba²⁺(aq) + 2OH⁻(aq).
c(Ba(OH)₂) = 0.050 M.
From chemical reaction: n(Ba(OH)₂) : n(OH⁻) = 1 : 2.
c(OH⁻) = 0.10 M = 10⁻¹ M.
c(OH⁻) · c(H₃O⁺) = 1·10⁻¹⁴ M².
c(H₃O⁺) = 10⁻¹⁴ M² ÷ 10⁻¹ M.
c(H₃O⁺) = 10⁻¹³ M.