Simplify cube root of 8g^3k^8

$\sqrt[3]{8 g^{3} k^{8}}$

Step 1

Rewrite $8 g^{3} k^{8}$ as ${(2 g k^{2})}^{3} k^{2}$ .

Rewrite $8$ as $2^{3}$ .

$\sqrt[3]{2^{3} g^{3} k^{8}}$

Factor out $k^{6}$ .

$\sqrt[3]{2^{3} g^{3} (k^{6} k^{2})}$

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

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

Rewrite $2^{3} g^{3} {(k^{2})}^{3}$ as ${(2 g k^{2})}^{3}$ .

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

Step 2

Pull terms out from under the radical.

$2 g k^{2} \sqrt[3]{k^{2}}$