Algebra Examples

$\sqrt[3]{50 x^{2} z^{5}} \cdot \sqrt[3]{15 y^{3} z}$

Step 1

Rewrite $50 x^{2} z^{5}$ as $z^{3} \cdot (50 x^{2} z^{2})$ .

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Step 1.1

Factor out $z^{3}$ .

$\sqrt[3]{50 x^{2} (z^{3} z^{2})} \cdot \sqrt[3]{15 y^{3} z}$

Step 1.2

Move $x^{2}$ .

$\sqrt[3]{50 z^{3} x^{2} z^{2}} \cdot \sqrt[3]{15 y^{3} z}$

Step 1.3

Reorder $50$ and $z^{3}$ .

$\sqrt[3]{z^{3} \cdot 50 x^{2} z^{2}} \cdot \sqrt[3]{15 y^{3} z}$

Step 1.4

Add parentheses.

$\sqrt[3]{z^{3} \cdot 50 (x^{2} z^{2})} \cdot \sqrt[3]{15 y^{3} z}$

Step 1.5

Add parentheses.

$\sqrt[3]{z^{3} \cdot (50 x^{2} z^{2})} \cdot \sqrt[3]{15 y^{3} z}$

Step 2

Pull terms out from under the radical.

$z \sqrt[3]{50 x^{2} z^{2}} \cdot \sqrt[3]{15 y^{3} z}$

Step 3

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

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Step 3.1

Reorder $15$ and $y^{3}$ .

$z \sqrt[3]{50 x^{2} z^{2}} \cdot \sqrt[3]{y^{3} \cdot 15 z}$

Step 3.2

Add parentheses.

$z \sqrt[3]{50 x^{2} z^{2}} \cdot \sqrt[3]{y^{3} \cdot (15 z)}$

Step 4

Pull terms out from under the radical.

$z \sqrt[3]{50 x^{2} z^{2}} \cdot (y \sqrt[3]{15 z})$

Step 5

Multiply $z \sqrt[3]{50 x^{2} z^{2}} (y \sqrt[3]{15 z})$ .

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Step 5.1

Combine using the product rule for radicals.

$z (y \sqrt[3]{50 x^{2} z^{2} (15 z)})$

Step 5.2

Multiply $15$ by $50$ .

$z (y \sqrt[3]{750 x^{2} z^{2} z})$

Step 5.3

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

$z (y \sqrt[3]{750 x^{2} (z^{1} z^{2})})$

Step 5.4

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

$z (y \sqrt[3]{750 x^{2} z^{1 + 2}})$

Step 5.5

Add $1$ and $2$ .

$z (y \sqrt[3]{750 x^{2} z^{3}})$

Step 6

Rewrite $750 x^{2} z^{3}$ as ${(5 z)}^{3} \cdot (6 x^{2})$ .

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Step 6.1

Factor $125$ out of $750$ .

$z (y \sqrt[3]{125 (6) x^{2} z^{3}})$

Step 6.2

Rewrite $125$ as $5^{3}$ .

$z (y \sqrt[3]{5^{3} \cdot 6 x^{2} z^{3}})$

Step 6.3

Move $x^{2}$ .

$z (y \sqrt[3]{5^{3} \cdot 6 z^{3} x^{2}})$

Step 6.4

Move $6$ .

$z (y \sqrt[3]{5^{3} z^{3} \cdot 6 x^{2}})$

Step 6.5

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

$z (y \sqrt[3]{{(5 z)}^{3} \cdot 6 x^{2}})$

Step 6.6

Add parentheses.

$z (y \sqrt[3]{{(5 z)}^{3} \cdot (6 x^{2})})$

Step 7

Pull terms out from under the radical.

$z (y (5 z \sqrt[3]{6 x^{2}}))$

Step 8

Rewrite using the commutative property of multiplication.

$5 z (y z \sqrt[3]{6 x^{2}})$

Step 9

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

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Step 9.1

Move $z$ .

$5 (z \cdot z) (y \sqrt[3]{6 x^{2}})$

Step 9.2

Multiply $z$ by $z$ .

$5 z^{2} (y \sqrt[3]{6 x^{2}})$

$5 z^{2} y \sqrt[3]{6 x^{2}}$