Simplify ( cube root of z)( cube root of 9z^4)

$(\sqrt[3]{z}) (\sqrt[3]{9 z^{4}})$

Rewrite $9 z^{4}$ as $z^{3} \cdot (9 z)$ .

Factor out $z^{3}$ .

$\sqrt[3]{z} \sqrt[3]{9 (z^{3} z)}$

Reorder $9$ and $z^{3}$ .

$\sqrt[3]{z} \sqrt[3]{z^{3} \cdot 9 z}$

Add parentheses.

$\sqrt[3]{z} \sqrt[3]{z^{3} \cdot (9 z)}$

Pull terms out from under the radical.

$\sqrt[3]{z} (z \sqrt[3]{9 z})$

Multiply $\sqrt[3]{z} (z \sqrt[3]{9 z})$ .

Combine using the product rule for radicals.

$z \sqrt[3]{z (9 z)}$

Raise $z$ to the power of $1$ .

$z \sqrt[3]{9 (z^{1} z)}$

Raise $z$ to the power of $1$ .

$z \sqrt[3]{9 (z^{1} z^{1})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$z \sqrt[3]{9 z^{1 + 1}}$

Add $1$ and $1$ .

$z \sqrt[3]{9 z^{2}}$