$\sqrt[6]{x^4 y^2 z^{-2}}$ in exponent form is—

Converting the root gives $x^{4/6}y^{2/6}z^{-2/6}$, and reducing each fraction yields $x^{2/3}y^{1/3}z^{-1/3}$. Both forms are equal, so both (a) and (b) are correct.