| 1) [4]√(ab^3)÷[12]√(a^6b)×[6]√(a^2b^(-4)) =[4]√(ab^3)×{1/[12]√(a^6b)}×[6]√(a^2b^(-4)) =a^(1/4)b^(3/4)×a^(-1/2)b^(-1/12)×a^(1/3)b^(-2/3) =a^(1/4-1/2+1/3)b^(3/4-1/12-2/3) =a^(1/12) =[12]√a
2) √√√a =√√(a^(1/2)) =√a^(1/4) =a^(1/8) =[8]√a
3) [3]√5÷[12]√5×[8]√25 =5^(1/3)×5^(-1/12)×25^(1/8) =5^(1/3)×5^(-1/12)×5^(1/4) =5^(1/3-1/12+1/4) =5^(1/2) =√5
4) [3]√81+[3]√3+[3]√-24 =81^(1/3)+3^(1/3)+(-24)^(1/3) =3^(4/3)+3^(1/3)-2*3^(1/3) =3^(4/3)-3^(1/3) =3^(1/3)*(3-1) =2[3]√3
|