Algebra Examples

$(\sqrt[3]{256 y^{8}}) (\sqrt[3]{625 y^{5}})$

Step 1

Rewrite $256 y^{8}$ as ${(4 y^{2})}^{3} \cdot (4 y^{2})$ .

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Step 1.1

Factor $64$ out of $256$ .

$\sqrt[3]{64 (4) y^{8}} \sqrt[3]{625 y^{5}}$

Step 1.2

Rewrite $64$ as $4^{3}$ .

$\sqrt[3]{4^{3} \cdot 4 y^{8}} \sqrt[3]{625 y^{5}}$

Step 1.3

Factor out $y^{6}$ .

$\sqrt[3]{4^{3} \cdot 4 (y^{6} y^{2})} \sqrt[3]{625 y^{5}}$

Step 1.4

Rewrite $y^{6}$ as ${(y^{2})}^{3}$ .

$\sqrt[3]{4^{3} \cdot 4 ({(y^{2})}^{3} y^{2})} \sqrt[3]{625 y^{5}}$

Step 1.5

Move $4$ .

$\sqrt[3]{4^{3} {(y^{2})}^{3} \cdot 4 y^{2}} \sqrt[3]{625 y^{5}}$

Step 1.6

Rewrite $4^{3} {(y^{2})}^{3}$ as ${(4 y^{2})}^{3}$ .

$\sqrt[3]{{(4 y^{2})}^{3} \cdot 4 y^{2}} \sqrt[3]{625 y^{5}}$

Step 1.7

Add parentheses.

$\sqrt[3]{{(4 y^{2})}^{3} \cdot (4 y^{2})} \sqrt[3]{625 y^{5}}$

Step 2

Pull terms out from under the radical.

$4 y^{2} \sqrt[3]{4 y^{2}} \sqrt[3]{625 y^{5}}$

Step 3

Rewrite $625 y^{5}$ as ${(5 y)}^{3} \cdot (5 y^{2})$ .

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Step 3.1

Factor $125$ out of $625$ .

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

Step 3.2

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

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

Step 3.3

Factor out $y^{3}$ .

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

Step 3.4

Move $5$ .

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

Step 3.5

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

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

Step 3.6

Add parentheses.

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

Step 4

Pull terms out from under the radical.

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

Step 5

Multiply $y^{2}$ by $y$ by adding the exponents.

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Step 5.1

Move $y$ .

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

Step 5.2

Multiply $y$ by $y^{2}$ .

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Step 5.2.1

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

$4 (y^{1} y^{2}) \sqrt[3]{4 y^{2}} (5 \sqrt[3]{5 y^{2}})$

Step 5.2.2

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

$4 y^{1 + 2} \sqrt[3]{4 y^{2}} (5 \sqrt[3]{5 y^{2}})$

Step 5.3

Add $1$ and $2$ .

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

Step 6

Multiply $4 y^{3} \sqrt[3]{4 y^{2}} (5 \sqrt[3]{5 y^{2}})$ .

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Step 6.1

Multiply $5$ by $4$ .

$20 y^{3} \sqrt[3]{4 y^{2}} \sqrt[3]{5 y^{2}}$

Step 6.2

Combine using the product rule for radicals.

$20 y^{3} \sqrt[3]{5 y^{2} (4 y^{2})}$

Step 6.3

Multiply $4$ by $5$ .

$20 y^{3} \sqrt[3]{20 y^{2} y^{2}}$

Step 6.4

Multiply $y^{2}$ by $y^{2}$ by adding the exponents.

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Step 6.4.1

Move $y^{2}$ .

$20 y^{3} \sqrt[3]{20 (y^{2} y^{2})}$

Step 6.4.2

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

$20 y^{3} \sqrt[3]{20 y^{2 + 2}}$

Step 6.4.3

Add $2$ and $2$ .

$20 y^{3} \sqrt[3]{20 y^{4}}$

Step 7

Rewrite $20 y^{4}$ as $y^{3} \cdot (20 y)$ .

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Step 7.1

Factor out $y^{3}$ .

$20 y^{3} \sqrt[3]{20 (y^{3} y)}$

Step 7.2

Reorder $20$ and $y^{3}$ .

$20 y^{3} \sqrt[3]{y^{3} \cdot 20 y}$

Step 7.3

Add parentheses.

$20 y^{3} \sqrt[3]{y^{3} \cdot (20 y)}$

Step 8

Pull terms out from under the radical.

$20 y^{3} (y \sqrt[3]{20 y})$

Step 9

Multiply $y^{3}$ by $y$ by adding the exponents.

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Step 9.1

Move $y$ .

$20 (y \cdot y^{3}) \sqrt[3]{20 y}$

Step 9.2

Multiply $y$ by $y^{3}$ .

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Step 9.2.1

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

$20 (y^{1} y^{3}) \sqrt[3]{20 y}$

Step 9.2.2

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

$20 y^{1 + 3} \sqrt[3]{20 y}$

Step 9.3

Add $1$ and $3$ .

$20 y^{4} \sqrt[3]{20 y}$