$$\left(8^\frac 12\right)^\frac{1}{3}=$$
$$\left(\sqrt{8}\right)^3$$
$$8^{\frac 12 +\frac 13}$$
$$8^{\frac 23}$$
$$\left( 8^\frac 13\right)^\frac 12$$
$$\sqrt{2}$$
$$8^\frac 16$$