Basic Math Examples

$\sqrt[3]{25 x^{5} y} \cdot 5 \sqrt[3]{10 x^{2} y^{4}}$

Step 1

Rewrite using the commutative property of multiplication.

$5 \sqrt[3]{25 x^{5} y} \sqrt[3]{10 x^{2} y^{4}}$

Step 2

Rewrite $25 x^{5} y$ as $x^{3} \cdot (25 x^{2} y)$ .

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Step 2.1

Factor out $x^{3}$ .

$5 \sqrt[3]{25 (x^{3} x^{2}) y} \sqrt[3]{10 x^{2} y^{4}}$

Step 2.2

Reorder $25$ and $x^{3}$ .

$5 \sqrt[3]{x^{3} \cdot 25 x^{2} y} \sqrt[3]{10 x^{2} y^{4}}$

Step 2.3

Add parentheses.

$5 \sqrt[3]{x^{3} \cdot 25 (x^{2} y)} \sqrt[3]{10 x^{2} y^{4}}$

Step 2.4

Add parentheses.

$5 \sqrt[3]{x^{3} \cdot (25 x^{2} y)} \sqrt[3]{10 x^{2} y^{4}}$

Step 3

Pull terms out from under the radical.

$5 (x \sqrt[3]{25 x^{2} y}) \sqrt[3]{10 x^{2} y^{4}}$

Step 4

Rewrite $10 x^{2} y^{4}$ as $y^{3} \cdot (10 x^{2} y)$ .

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Step 4.1

Factor out $y^{3}$ .

$5 x \sqrt[3]{25 x^{2} y} \sqrt[3]{10 x^{2} (y^{3} y)}$

Step 4.2

Move $x^{2}$ .

$5 x \sqrt[3]{25 x^{2} y} \sqrt[3]{10 y^{3} x^{2} y}$

Step 4.3

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

$5 x \sqrt[3]{25 x^{2} y} \sqrt[3]{y^{3} \cdot 10 x^{2} y}$

Step 4.4

Add parentheses.

$5 x \sqrt[3]{25 x^{2} y} \sqrt[3]{y^{3} \cdot 10 (x^{2} y)}$

Step 4.5

Add parentheses.

$5 x \sqrt[3]{25 x^{2} y} \sqrt[3]{y^{3} \cdot (10 x^{2} y)}$

Step 5

Pull terms out from under the radical.

$5 x \sqrt[3]{25 x^{2} y} (y \sqrt[3]{10 x^{2} y})$

Step 6

Multiply $5 x \sqrt[3]{25 x^{2} y} (y \sqrt[3]{10 x^{2} y})$ .

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Step 6.1

Combine using the product rule for radicals.

$5 x (y \sqrt[3]{25 x^{2} y (10 x^{2} y)})$

Step 6.2

Multiply $10$ by $25$ .

$5 x (y \sqrt[3]{250 x^{2} y (x^{2} y)})$

Step 6.3

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

$5 x (y \sqrt[3]{250 x^{2 + 2} y \cdot y})$

Step 6.4

Add $2$ and $2$ .

$5 x (y \sqrt[3]{250 x^{4} y \cdot y})$

Step 6.5

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

$5 x (y \sqrt[3]{250 x^{4} (y^{1} y)})$

Step 6.6

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

$5 x (y \sqrt[3]{250 x^{4} (y^{1} y^{1})})$

Step 6.7

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

$5 x (y \sqrt[3]{250 x^{4} y^{1 + 1}})$

Step 6.8

Add $1$ and $1$ .

$5 x (y \sqrt[3]{250 x^{4} y^{2}})$

Step 7

Rewrite $250 x^{4} y^{2}$ as ${(5 x)}^{3} \cdot (2 x y^{2})$ .

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Step 7.1

Factor $125$ out of $250$ .

$5 x (y \sqrt[3]{125 (2) x^{4} y^{2}})$

Step 7.2

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

$5 x (y \sqrt[3]{5^{3} \cdot 2 x^{4} y^{2}})$

Step 7.3

Factor out $x^{3}$ .

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

Step 7.4

Move $2$ .

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

Step 7.5

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

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

Step 7.6

Add parentheses.

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

Step 7.7

Add parentheses.

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

Step 8

Pull terms out from under the radical.

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

Step 9

Multiply $x$ by $x$ by adding the exponents.

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Step 9.1

Move $x$ .

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

Step 9.2

Multiply $x$ by $x$ .

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

Step 10

Rewrite using the commutative property of multiplication.

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

Step 11

Multiply $5$ by $5$ .

$25 x^{2} (y \sqrt[3]{2 x y^{2}})$

Step 12

Reorder factors in $25 x^{2} (y \sqrt[3]{2 x y^{2}})$ .

$25 x^{2} y \sqrt[3]{2 x y^{2}}$