#1**+2 **

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.

SUS101 Mar 9, 2019

#2**+1 **

As long as " a " ≥ 0....then

The cube root can be written as a^(1/3)

We are using the property that ( a^m)^n = a^(m * n)

So....the square root of a cube root is

(a^1/3)^(1/2) =

(a)^(1/2 * 1/3) =

a ^(1/6) .... i.e., the sixth root

This only holds as long as "a" ≥ 0

If "a" < 0.....the cube root of this is negative...then...... we are taking the square root of a negative.....which is not a real number

Does this make sense, GM ???

CPhill Mar 9, 2019