Simplify ( cube root of 80z)( cube root of 15z^8)

$(\sqrt[3]{80 z}) (\sqrt[3]{15 z^{8}})$

Rewrite $80 z$ as $2^{3} \cdot (10 z)$ .

Factor $8$ out of $80$ .

$\sqrt[3]{8 (10) z} \sqrt[3]{15 z^{8}}$

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

$\sqrt[3]{2^{3} \cdot 10 z} \sqrt[3]{15 z^{8}}$

Add parentheses.

$\sqrt[3]{2^{3} \cdot (10 z)} \sqrt[3]{15 z^{8}}$

Pull terms out from under the radical.

$2 \sqrt[3]{10 z} \sqrt[3]{15 z^{8}}$

Rewrite $15 z^{8}$ as ${(z^{2})}^{3} \cdot (15 z^{2})$ .

Factor out $z^{6}$ .

$2 \sqrt[3]{10 z} \sqrt[3]{15 (z^{6} z^{2})}$

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

$2 \sqrt[3]{10 z} \sqrt[3]{15 ({(z^{2})}^{3} z^{2})}$

Reorder $15$ and ${(z^{2})}^{3}$ .

$2 \sqrt[3]{10 z} \sqrt[3]{{(z^{2})}^{3} \cdot 15 z^{2}}$

Add parentheses.

$2 \sqrt[3]{10 z} \sqrt[3]{{(z^{2})}^{3} \cdot (15 z^{2})}$

Pull terms out from under the radical.

$2 \sqrt[3]{10 z} (z^{2} \sqrt[3]{15 z^{2}})$

Multiply $2 \sqrt[3]{10 z} (z^{2} \sqrt[3]{15 z^{2}})$ .

Combine using the product rule for radicals.

$2 (z^{2} \sqrt[3]{10 z (15 z^{2})})$

Multiply $15$ by $10$ .

$2 (z^{2} \sqrt[3]{150 z \cdot z^{2}})$

Multiply $z$ by $z^{2}$ by adding the exponents.

Move $z^{2}$ .

$2 (z^{2} \sqrt[3]{150 (z^{2} z)})$

Multiply $z^{2}$ by $z$ .

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

$2 (z^{2} \sqrt[3]{150 (z^{2} z^{1})})$

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

$2 (z^{2} \sqrt[3]{150 z^{2 + 1}})$

Add $2$ and $1$ .

$2 (z^{2} \sqrt[3]{150 z^{3}})$

Reorder $150$ and $z^{3}$ .

$2 (z^{2} \sqrt[3]{z^{3} \cdot 150})$

Pull terms out from under the radical.

$2 (z^{2} (z \sqrt[3]{150}))$

Multiply $z^{2}$ by $z$ by adding the exponents.

Move $z$ .

$2 (z \cdot z^{2} \sqrt[3]{150})$

Multiply $z$ by $z^{2}$ .

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

$2 (z^{1} z^{2} \sqrt[3]{150})$

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

$2 (z^{1 + 2} \sqrt[3]{150})$

Add $1$ and $2$ .

$2 (z^{3} \sqrt[3]{150})$

$2 z^{3} \sqrt[3]{150}$

Simplify ( cube root of 80z)( cube root of 15z^8)

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