We have: root(3)(frac(3 a^(8))(4 b))3√3a84b
= frac(root(3)(3 a^(8)))(root(3)(4 b))=3√3a83√4b
= frac(root(3)(3 a^(8)))(root(3)(4 b)) cdot frac(root(3)(4 b))(root(3)(4 b)) cdot frac(root(3)(4 b))(root(3)(4 b))=3√3a83√4b⋅3√4b3√4b⋅3√4b3√4b
= frac(root(3)(48 a^(8) b^(2)))(4 b)=3√48a8b24b
= frac(root(3)(48) cdot root(3)(a^(8)) cdot root(3)(b^(2)))(4 b)=3√48⋅3√a8⋅3√b24b
= frac(root(3)(2 cdot 2 cdot 2 cdot 6) cdot root(3)(a^(8)) cdot root(3)(b^(2)))(4 b)=3√2⋅2⋅2⋅6⋅3√a8⋅3√b24b
= frac(root(3)(2 cdot 2 cdot 2) cdot root(3)(6) cdot root(3)(a^(8)) cdot root(3)(b^(2)))(4 b)=3√2⋅2⋅2⋅3√6⋅3√a8⋅3√b24b
= frac(2 root(3)(6 a^(8) b^(2)))(4 b)=23√6a8b24b
= frac(root(3)(6 a^(8) b^(2)))(2 b)=3√6a8b22b