Simplify fourth root of x^(2/3)

$\sqrt[4]{x^{\frac{2}{3}}}$

Rewrite $x^{\frac{2}{3}}$ as ${(x^{\frac{1}{3}})}^{2}$ .

$\sqrt[4]{{(x^{\frac{1}{3}})}^{2}}$

Rewrite $\sqrt[4]{{(x^{\frac{1}{3}})}^{2}}$ as $\sqrt{\sqrt{{(x^{\frac{1}{3}})}^{2}}}$ .

$\sqrt{\sqrt{{(x^{\frac{1}{3}})}^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

$\sqrt{x^{\frac{1}{3}}}$