Verified answer

3∛8 + 4*⁵√-32 + ⁴√625 = 3∛2³ + 4*⁵√(-2)⁵ + ⁴√5⁴ = 3*2 + 4*(-2) + 5 = 6 - 8 + 5 = 3

⁴√2¹²*5⁸ = ⁴√(2³)⁴*(5²)⁴ = = 2³*5² = 8*25 = 200

1/∛9 = 1/3^2/3 = 3^1/3/3 = ∛3/3

4/(∛7 - ∛3) = 4(∛7² +  ∛7*4 + ∛3²) /(7 - 3) = ∛7² +  ∛7*4 + ∛3² = ∛49 +  ∛28 + ∛9

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(a^m)^n = a^mn

a^1/3 = ∛a

a³ - b³ = (a-b)(a²+ab+b²)