Simplify cube root of fourth root of x^36

$\sqrt[3]{\sqrt[4]{x^{36}}}$

Rewrite $x^{36}$ as ${(x^{9})}^{4}$ .

$\sqrt[3]{\sqrt[4]{{(x^{9})}^{4}}}$

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

$\sqrt[3]{x^{9}}$

Rewrite $x^{9}$ as ${(x^{3})}^{3}$ .

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

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

$x^{3}$