Simplify 12 cube root of 2z^5-z cube root of 54z^3

$12 \sqrt[3]{2 z^{5}} - z \sqrt[3]{54 z^{3}}$

Rewrite $2 z^{5}$ as $z^{3} \cdot (2 z^{2})$ .

Factor out $z^{3}$ .

$12 \sqrt[3]{2 (z^{3} z^{2})} - z \sqrt[3]{54 z^{3}}$

Reorder $2$ and $z^{3}$ .

$12 \sqrt[3]{z^{3} \cdot 2 z^{2}} - z \sqrt[3]{54 z^{3}}$

Add parentheses.

$12 \sqrt[3]{z^{3} \cdot (2 z^{2})} - z \sqrt[3]{54 z^{3}}$

Pull terms out from under the radical.

$12 (z \sqrt[3]{2 z^{2}}) - z \sqrt[3]{54 z^{3}}$

Rewrite $54 z^{3}$ as ${(3 z)}^{3} \cdot 2$ .

Factor $27$ out of $54$ .

$12 z \sqrt[3]{2 z^{2}} - z \sqrt[3]{27 (2) z^{3}}$

Rewrite $27$ as $3^{3}$ .

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

Move $2$ .

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

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

$12 z \sqrt[3]{2 z^{2}} - z \sqrt[3]{{(3 z)}^{3} \cdot 2}$

Pull terms out from under the radical.

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

Multiply $z$ by $z$ by adding the exponents.

Move $z$ .

$12 z \sqrt[3]{2 z^{2}} - (z \cdot z) (3 \sqrt[3]{2})$

Multiply $z$ by $z$ .

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

Multiply $3$ by $- 1$ .

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