Precalculus Examples

$2 x \sqrt[3]{54 x^{4}} + 4 \sqrt[3]{16 x^{7}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $54 x^{4}$ as ${(3 x)}^{3} \cdot (2 x)$ .

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Step 1.1.1

Factor $27$ out of $54$ .

$2 x \sqrt[3]{27 (2) x^{4}} + 4 \sqrt[3]{16 x^{7}}$

Step 1.1.2

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

$2 x \sqrt[3]{3^{3} \cdot 2 x^{4}} + 4 \sqrt[3]{16 x^{7}}$

Step 1.1.3

Factor out $x^{3}$ .

$2 x \sqrt[3]{3^{3} \cdot 2 (x^{3} x)} + 4 \sqrt[3]{16 x^{7}}$

Step 1.1.4

Move $2$ .

$2 x \sqrt[3]{3^{3} x^{3} \cdot 2 x} + 4 \sqrt[3]{16 x^{7}}$

Step 1.1.5

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

$2 x \sqrt[3]{{(3 x)}^{3} \cdot 2 x} + 4 \sqrt[3]{16 x^{7}}$

Step 1.1.6

Add parentheses.

$2 x \sqrt[3]{{(3 x)}^{3} \cdot (2 x)} + 4 \sqrt[3]{16 x^{7}}$

Step 1.2

Pull terms out from under the radical.

$2 x (3 x \sqrt[3]{2 x}) + 4 \sqrt[3]{16 x^{7}}$

Step 1.3

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

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Step 1.3.1

Move $x$ .

$2 (x \cdot x) (3 \sqrt[3]{2 x}) + 4 \sqrt[3]{16 x^{7}}$

Step 1.3.2

Multiply $x$ by $x$ .

$2 x^{2} (3 \sqrt[3]{2 x}) + 4 \sqrt[3]{16 x^{7}}$

Step 1.4

Multiply $3$ by $2$ .

$6 x^{2} \sqrt[3]{2 x} + 4 \sqrt[3]{16 x^{7}}$

Step 1.5

Rewrite $16 x^{7}$ as ${(2 x^{2})}^{3} \cdot (2 x)$ .

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Step 1.5.1

Factor $8$ out of $16$ .

$6 x^{2} \sqrt[3]{2 x} + 4 \sqrt[3]{8 (2) x^{7}}$

Step 1.5.2

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

$6 x^{2} \sqrt[3]{2 x} + 4 \sqrt[3]{2^{3} \cdot 2 x^{7}}$

Step 1.5.3

Factor out $x^{6}$ .

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

Step 1.5.4

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

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

Step 1.5.5

Move $2$ .

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

Step 1.5.6

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

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

Step 1.5.7

Add parentheses.

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

Step 1.6

Pull terms out from under the radical.

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

Step 1.7

Multiply $2$ by $4$ .

$6 x^{2} \sqrt[3]{2 x} + 8 x^{2} \sqrt[3]{2 x}$

Step 2

Add $6 x^{2} \sqrt[3]{2 x}$ and $8 x^{2} \sqrt[3]{2 x}$ .

$14 x^{2} \sqrt[3]{2 x}$