Basic Math Examples

$\sqrt[3]{4 z^{2} y} \cdot \sqrt[3]{10 z y^{3}}$

Step 1

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

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Step 1.1

Move $z$ .

$\sqrt[3]{4 z^{2} y} \cdot \sqrt[3]{10 y^{3} z}$

Step 1.2

Reorder $10$ and $y^{3}$ .

$\sqrt[3]{4 z^{2} y} \cdot \sqrt[3]{y^{3} \cdot 10 z}$

Step 1.3

Add parentheses.

$\sqrt[3]{4 z^{2} y} \cdot \sqrt[3]{y^{3} \cdot (10 z)}$

Step 2

Pull terms out from under the radical.

$\sqrt[3]{4 z^{2} y} \cdot (y \sqrt[3]{10 z})$

Step 3

Multiply $\sqrt[3]{4 z^{2} y} (y \sqrt[3]{10 z})$ .

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Step 3.1

Combine using the product rule for radicals.

$y \sqrt[3]{4 z^{2} y (10 z)}$

Step 3.2

Multiply $10$ by $4$ .

$y \sqrt[3]{40 z^{2} y z}$

Step 3.3

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

$y \sqrt[3]{40 y (z^{2} z^{1})}$

Step 3.4

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

$y \sqrt[3]{40 y z^{2 + 1}}$

Step 3.5

Add $2$ and $1$ .

$y \sqrt[3]{40 y z^{3}}$

Step 4

Rewrite $40 y z^{3}$ as ${(2 z)}^{3} \cdot (5 y)$ .

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Step 4.1

Factor $8$ out of $40$ .

$y \sqrt[3]{8 (5) y z^{3}}$

Step 4.2

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

$y \sqrt[3]{2^{3} \cdot 5 y z^{3}}$

Step 4.3

Move $y$ .

$y \sqrt[3]{2^{3} \cdot 5 z^{3} y}$

Step 4.4

Move $5$ .

$y \sqrt[3]{2^{3} z^{3} \cdot 5 y}$

Step 4.5

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

$y \sqrt[3]{{(2 z)}^{3} \cdot 5 y}$

Step 4.6

Add parentheses.

$y \sqrt[3]{{(2 z)}^{3} \cdot (5 y)}$

Step 5

Pull terms out from under the radical.

$y (2 z \sqrt[3]{5 y})$

Step 6

Rewrite using the commutative property of multiplication.

$2 y z \sqrt[3]{5 y}$