Algebra Examples

$\sqrt[3]{4 x^{2}} \cdot \sqrt[3]{8 x^{7}}$

Step 1

Rewrite $8 x^{7}$ as ${(2 x^{2})}^{3} x$ .

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Step 1.1

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

$\sqrt[3]{4 x^{2}} \cdot \sqrt[3]{2^{3} x^{7}}$

Step 1.2

Factor out $x^{6}$ .

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

Step 1.3

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

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

Step 1.4

Rewrite $2^{3} {(x^{2})}^{3}$ as ${(2 x^{2})}^{3}$ .

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

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

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Step 4.1

Combine using the product rule for radicals.

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

Step 4.2

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

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

Step 4.3

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

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

Step 4.4

Add $1$ and $2$ .

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

Step 5

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

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

Step 6

Pull terms out from under the radical.

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

Step 7

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

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Step 7.1

Move $x$ .

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

Step 7.2

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

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Step 7.2.1

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

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

Step 7.2.2

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

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

Step 7.3

Add $1$ and $2$ .

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

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