Verified answer

a^m^a^n = a^(m + n)

(a^m)^n = a^(mn)

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⁵√a * a^4/5 = a^1/5*a^4/5 = a^(1/5 + 4/5) = a^1

⁶√x³ : x^1/2 = x*3/6 : x^1/2 = x^1/2 : x^1/2 = 1^1

∛(2^-1) ³ = (2^-1)^3*1/3 = 2^-1

(3³)^1/3 = 3^(3*1/3) = 3^1