Simplify square root of cube root of x^10

$\sqrt{\sqrt[3]{x^{10}}}$

Rewrite $x^{10}$ as ${(x^{3})}^{3} x$ .

Factor out $x^{9}$ .

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

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

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

Pull terms out from under the radical.

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

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

Factor out $x^{2}$ .

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

Add parentheses.

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

Pull terms out from under the radical.

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