Yes she is correct because when you convert it into exponential value like so: \((a^{1/3})^{1/2}\) and then use the Product Property of Exponents you get \(a^{1/6}\) which is equivelent to the 6th root. Also lets say a is 64 and you take the cube root and get 4 and then take the square root of 4 and get 2. Also the 6th oot of 64 is 2. So this shows that they are both equal.