Which of the following statements is true ?

Let's compare the values by raising both expressions to the power of $6$ (the LCM of the denominators of the powers $2$ and $3$):
$$\text{Value 1}={\left[{\left(\frac{1}{2}\right)}^{1/2}\right]}^6={\left(\frac{1}{2}\right)}^3=\frac{1}{8}=0.125$$
$$\text{Value 2}={\left[{\left(\frac{1}{3}\right)}^{1/3}\right]}^6={\left(\frac{1}{3}\right)}^2=\frac{1}{9}\approx 0.111$$
Since $0.125>0.111$:
$${\left(\frac{1}{2}\right)}^{1/2}>{\left(\frac{1}{3}\right)}^{1/3}$$