Simplify fourth root of (k^16)/(16z^4)

$\sqrt[4]{\frac{k^{16}}{16 z^{4}}}$

Step 1

Rewrite $k^{16}$ as ${(k^{4})}^{4}$ .

$\sqrt[4]{\frac{{(k^{4})}^{4}}{16 z^{4}}}$

Step 2

Rewrite $16 z^{4}$ as ${(2 z)}^{4}$ .

$\sqrt[4]{\frac{{(k^{4})}^{4}}{{(2 z)}^{4}}}$

Step 3

Rewrite $\frac{{(k^{4})}^{4}}{{(2 z)}^{4}}$ as ${(\frac{k^{4}}{2 z})}^{4}$ .

$\sqrt[4]{{(\frac{k^{4}}{2 z})}^{4}}$

Step 4

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

$\frac{k^{4}}{2 z}$