Algebra Examples

$(\sqrt[3]{4 b^{8}}) (\sqrt[3]{4 b^{3}})$

Step 1

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

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Step 1.1

Factor out $b^{6}$ .

$\sqrt[3]{4 (b^{6} b^{2})} \sqrt[3]{4 b^{3}}$

Step 1.2

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

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

Step 1.3

Reorder $4$ and ${(b^{2})}^{3}$ .

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

Step 1.4

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$b^{2} \sqrt[3]{4 b^{2}} \sqrt[3]{4 b^{3}}$

Step 3

Reorder $4$ and $b^{3}$ .

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

Step 4

Pull terms out from under the radical.

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

Step 5

Rewrite using the commutative property of multiplication.

$\sqrt[3]{4} b^{2} \sqrt[3]{4 b^{2}} b$

Step 6

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

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Step 6.1

Move $b$ .

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

Step 6.2

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

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Step 6.2.1

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

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

Step 6.2.2

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

$\sqrt[3]{4} b^{1 + 2} \sqrt[3]{4 b^{2}}$

Step 6.3

Add $1$ and $2$ .

$\sqrt[3]{4} b^{3} \sqrt[3]{4 b^{2}}$

Step 7

Multiply $\sqrt[3]{4} b^{3} \sqrt[3]{4 b^{2}}$ .

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Step 7.1

Combine using the product rule for radicals.

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

Step 7.2

Multiply $4$ by $4$ .

$b^{3} \sqrt[3]{4^{2} b^{2}}$

Step 8

Raise $4$ to the power of $2$ .

$b^{3} \sqrt[3]{16 b^{2}}$

Step 9

Rewrite $16 b^{2}$ as $2^{3} \cdot (2 b^{2})$ .

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Step 9.1

Factor $8$ out of $16$ .

$b^{3} \sqrt[3]{8 (2) b^{2}}$

Step 9.2

Rewrite $8$ as $2^{3}$ .

$b^{3} \sqrt[3]{2^{3} \cdot 2 b^{2}}$

Step 9.3

Add parentheses.

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

Step 10

Pull terms out from under the radical.

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

Step 11

Rewrite using the commutative property of multiplication.

$2 b^{3} \sqrt[3]{2 b^{2}}$