Algebra Examples

$(\sqrt[3]{128 r^{4}}) (\sqrt[3]{108 r})$

Step 1

Rewrite $128 r^{4}$ as ${(4 r)}^{3} \cdot (2 r)$ .

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Step 1.1

Factor $64$ out of $128$ .

$\sqrt[3]{64 (2) r^{4}} \sqrt[3]{108 r}$

Step 1.2

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

$\sqrt[3]{4^{3} \cdot 2 r^{4}} \sqrt[3]{108 r}$

Step 1.3

Factor out $r^{3}$ .

$\sqrt[3]{4^{3} \cdot 2 (r^{3} r)} \sqrt[3]{108 r}$

Step 1.4

Move $2$ .

$\sqrt[3]{4^{3} r^{3} \cdot 2 r} \sqrt[3]{108 r}$

Step 1.5

Rewrite $4^{3} r^{3}$ as ${(4 r)}^{3}$ .

$\sqrt[3]{{(4 r)}^{3} \cdot 2 r} \sqrt[3]{108 r}$

Step 1.6

Add parentheses.

$\sqrt[3]{{(4 r)}^{3} \cdot (2 r)} \sqrt[3]{108 r}$

Step 2

Pull terms out from under the radical.

$4 r \sqrt[3]{2 r} \sqrt[3]{108 r}$

Step 3

Rewrite $108 r$ as $3^{3} \cdot (4 r)$ .

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Step 3.1

Factor $27$ out of $108$ .

$4 r \sqrt[3]{2 r} \sqrt[3]{27 (4) r}$

Step 3.2

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

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

Step 3.3

Add parentheses.

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

Step 4

Pull terms out from under the radical.

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

Step 5

Multiply $4 r \sqrt[3]{2 r} (3 \sqrt[3]{4 r})$ .

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Step 5.1

Multiply $3$ by $4$ .

$12 r \sqrt[3]{2 r} \sqrt[3]{4 r}$

Step 5.2

Combine using the product rule for radicals.

$12 r \sqrt[3]{4 r (2 r)}$

Step 5.3

Multiply $2$ by $4$ .

$12 r \sqrt[3]{8 r \cdot r}$

Step 5.4

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

$12 r \sqrt[3]{8 (r^{1} r)}$

Step 5.5

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

$12 r \sqrt[3]{8 (r^{1} r^{1})}$

Step 5.6

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

$12 r \sqrt[3]{8 r^{1 + 1}}$

Step 5.7

Add $1$ and $1$ .

$12 r \sqrt[3]{8 r^{2}}$

Step 6

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

$12 r \sqrt[3]{2^{3} r^{2}}$

Step 7

Pull terms out from under the radical.

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

Step 8

Multiply $2$ by $12$ .

$24 r \sqrt[3]{r^{2}}$