Используем свойства
a²-b²=(a-b)(a+b)
a³-b³=(a-b)(a²+ab+b²)
ᵃ√ᵇ√x = ᵃᵇ√x
xᵃxᵇ = xᵃ⁺ᵇ
(xᵃ)ᵇ = xᵃᵇ
ᵃ√xᵇ = x^(b/a)
1
(√a - ∛b²)/(⁴√a - ∛b) = ((⁴√a)² - (∛b)²)/(⁴√a - ∛b) = (⁴√a - ∛b) (⁴√a + ∛b)/(⁴√a - ∛b) = ⁴√a + ∛b
(⁵√x⁹ - 1)/(⁵√x - 1) = ((⁵√x³)³ - 1³))/(⁵√x³ - 1) = (⁵√x³ - 1)(⁵√x⁶+⁵√x³+1)/(⁵√x³ - 1) = ⁵√x⁶+⁵√x³+1
2
⁴√2∛(2m⁴n⁸) = ⁴√∛(2³2m⁴n⁸) = ¹²√(2⁴m⁴n⁸) = ∛(2mn²)
√y ⁵√(9x⁴y²) = √⁵√(y⁵*9x⁴y²) = ¹⁰√(9x⁴y⁵⁺²) = ¹⁰√(9x⁴y⁷)