Trigonometry Examples

$(\sqrt[3]{27 x^{2}}) (\sqrt[3]{16 x^{4}})$

Step 1

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

$\sqrt[3]{3^{3} x^{2}} \sqrt[3]{16 x^{4}}$

Step 2

Pull terms out from under the radical.

$3 \sqrt[3]{x^{2}} \sqrt[3]{16 x^{4}}$

Step 3

Rewrite $16 x^{4}$ as ${(2 x)}^{3} \cdot (2 x)$ .

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Step 3.1

Factor $8$ out of $16$ .

$3 \sqrt[3]{x^{2}} \sqrt[3]{8 (2) x^{4}}$

Step 3.2

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

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

Step 3.3

Factor out $x^{3}$ .

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

Step 3.4

Move $2$ .

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

Step 3.5

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

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

Step 3.6

Add parentheses.

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

Step 4

Pull terms out from under the radical.

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

Step 5

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

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Step 5.1

Multiply $2$ by $3$ .

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

Step 5.2

Combine using the product rule for radicals.

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

Step 5.3

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

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Step 5.3.1

Move $x$ .

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

Step 5.3.2

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

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Step 5.3.2.1

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

$6 (x \sqrt[3]{x^{1} x^{2} \cdot 2})$

Step 5.3.2.2

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

$6 (x \sqrt[3]{x^{1 + 2} \cdot 2})$

Step 5.3.3

Add $1$ and $2$ .

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

Step 6

Pull terms out from under the radical.

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

Step 7

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

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Step 7.1

Move $x$ .

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

Step 7.2

Multiply $x$ by $x$ .

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

$6 x^{2} \sqrt[3]{2}$