Simplify f(x) = fourth root of fifth root of square root of x^17

$f (x) = \sqrt[4]{\sqrt[5]{\sqrt[2]{x^{17}}}}$

Rewrite $x^{17}$ as ${(x^{8})}^{2} x$ .

Factor out $x^{16}$ .

$f (x) = \sqrt[4]{\sqrt[5]{\sqrt{x^{16} x}}}$

Rewrite $x^{16}$ as ${(x^{8})}^{2}$ .

$f (x) = \sqrt[4]{\sqrt[5]{\sqrt{{(x^{8})}^{2} x}}}$

Pull terms out from under the radical.

$f (x) = \sqrt[4]{\sqrt[5]{x^{8} \sqrt{x}}}$

Rewrite $x^{8} \sqrt{x}$ as $x^{5} (x^{3} \sqrt{x})$ .

Factor out $x^{5}$ .

$f (x) = \sqrt[4]{\sqrt[5]{x^{5} x^{3} \sqrt{x}}}$

Add parentheses.

$f (x) = \sqrt[4]{\sqrt[5]{x^{5} (x^{3} \sqrt{x})}}$

Pull terms out from under the radical.

$f (x) = \sqrt[4]{x \sqrt[5]{x^{3} \sqrt{x}}}$