Precalculus Examples

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

Step 1

Pull terms out from under the radical.

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

Step 2

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

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Step 2.1

Combine using the product rule for radicals.

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Add $1$ and $2$ .

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

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

Step 3

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

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Step 3.1

Move $y$ .

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

Step 3.2

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

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

Step 3.3

Add parentheses.

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

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

Step 4

Pull terms out from under the radical.

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

Step 5

Reorder factors in $y (z \sqrt[3]{2 y})$ .

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$