Algebra Examples

$12 \sqrt[3]{2 z^{5}} - z \sqrt[3]{54 z^{3}}$

Step 1

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

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Step 1.1

Factor out $z^{3}$ .

$12 \sqrt[3]{2 (z^{3} z^{2})} - z \sqrt[3]{54 z^{3}}$

Step 1.2

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

$12 \sqrt[3]{z^{3} \cdot 2 z^{2}} - z \sqrt[3]{54 z^{3}}$

Step 1.3

Add parentheses.

$12 \sqrt[3]{z^{3} \cdot (2 z^{2})} - z \sqrt[3]{54 z^{3}}$

Step 2

Pull terms out from under the radical.

$12 (z \sqrt[3]{2 z^{2}}) - z \sqrt[3]{54 z^{3}}$

Step 3

Rewrite $54 z^{3}$ as ${(3 z)}^{3} \cdot 2$ .

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Step 3.1

Factor $27$ out of $54$ .

$12 z \sqrt[3]{2 z^{2}} - z \sqrt[3]{27 (2) z^{3}}$

Step 3.2

Rewrite $27$ as $3^{3}$ .

$12 z \sqrt[3]{2 z^{2}} - z \sqrt[3]{3^{3} \cdot 2 z^{3}}$

Step 3.3

Move $2$ .

$12 z \sqrt[3]{2 z^{2}} - z \sqrt[3]{3^{3} z^{3} \cdot 2}$

Step 3.4

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

$12 z \sqrt[3]{2 z^{2}} - z \sqrt[3]{{(3 z)}^{3} \cdot 2}$

Step 4

Pull terms out from under the radical.

$12 z \sqrt[3]{2 z^{2}} - z (3 z \sqrt[3]{2})$

Step 5

Multiply $z$ by $z$ by adding the exponents.

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Step 5.1

Move $z$ .

$12 z \sqrt[3]{2 z^{2}} - (z \cdot z) (3 \sqrt[3]{2})$

Step 5.2

Multiply $z$ by $z$ .

$12 z \sqrt[3]{2 z^{2}} - z^{2} (3 \sqrt[3]{2})$

Step 6

Multiply $3$ by $- 1$ .

$12 z \sqrt[3]{2 z^{2}} - 3 z^{2} \sqrt[3]{2}$