Algebra Examples

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

Step 1

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

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Step 1.1

Factor out $z^{3}$ .

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

Step 1.2

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

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

Step 1.3

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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Step 3.1

Combine using the product rule for radicals.

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

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

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

Step 3.5

Add $1$ and $1$ .

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