Simplify ( cube root of 16z^6)( cube root of 6z)

$(\sqrt[3]{16 z^{6}}) (\sqrt[3]{6 z})$

Rewrite $16 z^{6}$ as ${(2 z^{2})}^{3} \cdot 2$ .

Factor $8$ out of $16$ .

$\sqrt[3]{8 (2) z^{6}} \sqrt[3]{6 z}$

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

$\sqrt[3]{2^{3} \cdot 2 z^{6}} \sqrt[3]{6 z}$

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

$\sqrt[3]{2^{3} \cdot 2 {(z^{2})}^{3}} \sqrt[3]{6 z}$

Move $2$ .

$\sqrt[3]{2^{3} {(z^{2})}^{3} \cdot 2} \sqrt[3]{6 z}$

Rewrite $2^{3} {(z^{2})}^{3}$ as ${(2 z^{2})}^{3}$ .

$\sqrt[3]{{(2 z^{2})}^{3} \cdot 2} \sqrt[3]{6 z}$

Pull terms out from under the radical.

$2 z^{2} \sqrt[3]{2} \sqrt[3]{6 z}$

Multiply $2 z^{2} \sqrt[3]{2} \sqrt[3]{6 z}$ .

Combine using the product rule for radicals.

$2 z^{2} \sqrt[3]{6 z \cdot 2}$

Multiply $2$ by $6$ .

$2 z^{2} \sqrt[3]{12 z}$