Simplify fourth root of square root of x^7

$\sqrt[4]{\sqrt[2]{x^{7}}}$

Step 1

Rewrite $x^{7}$ as ${(x^{3})}^{2} x$ .

Factor out $x^{6}$ .

$\sqrt[4]{\sqrt{x^{6} x}}$

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

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

Step 2

Pull terms out from under the radical.

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