Simplify 16 root of x^34

$\sqrt[16]{x^{34}}$

Step 1

Rewrite $x^{34}$ as ${(x^{2})}^{16} x^{2}$ .

Factor out $x^{32}$ .

$\sqrt[16]{x^{32} x^{2}}$

Rewrite $x^{32}$ as ${(x^{2})}^{16}$ .

$\sqrt[16]{{(x^{2})}^{16} x^{2}}$

Step 2

Pull terms out from under the radical.

$x^{2} \sqrt[16]{x^{2}}$

Step 3

Rewrite $\sqrt[16]{x^{2}}$ as $\sqrt[8]{\sqrt{x^{2}}}$ .

$x^{2} \sqrt[8]{\sqrt{x^{2}}}$

Step 4

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

$x^{2} \sqrt[8]{x}$