Verified answer

⁴√(9√10 - 18)*⁴√(6 + 3√10)*⁴√128 = ⁴√3(3√10 - 6 )(6 + 3√10)*⁴√2⁷ = ⁴√3(90 - 36)*⁴√2⁷ = ⁴√(3*54)*⁴√2⁷ = ⁴√(3*27*2)*⁴√2⁷ =  ⁴√(3*³*2)*⁴√2⁷ =  ⁴√(3⁴*2⁸) = 3*2² = 12