Simplify cube root of square root of x^24

$\sqrt[3]{\sqrt[2]{x^{24}}}$

Rewrite $x^{24}$ as ${(x^{12})}^{2}$ .

$\sqrt[3]{\sqrt{{(x^{12})}^{2}}}$

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

$\sqrt[3]{x^{12}}$

Rewrite $x^{12}$ as ${(x^{4})}^{3}$ .

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

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

$x^{4}$