Pre-Algebra Examples

$- 9 \sqrt[3]{81 x^{4}} - 5 x \sqrt[3]{24 x}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $81 x^{4}$ as ${(3 x)}^{3} \cdot (3 x)$ .

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Step 1.1.1

Factor $27$ out of $81$ .

$- 9 \sqrt[3]{27 (3) x^{4}} - 5 x \sqrt[3]{24 x}$

Step 1.1.2

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

$- 9 \sqrt[3]{3^{3} \cdot 3 x^{4}} - 5 x \sqrt[3]{24 x}$

Step 1.1.3

Factor out $x^{3}$ .

$- 9 \sqrt[3]{3^{3} \cdot 3 (x^{3} x)} - 5 x \sqrt[3]{24 x}$

Step 1.1.4

Move $3$ .

$- 9 \sqrt[3]{3^{3} x^{3} \cdot 3 x} - 5 x \sqrt[3]{24 x}$

Step 1.1.5

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

$- 9 \sqrt[3]{{(3 x)}^{3} \cdot 3 x} - 5 x \sqrt[3]{24 x}$

Step 1.1.6

Add parentheses.

$- 9 \sqrt[3]{{(3 x)}^{3} \cdot (3 x)} - 5 x \sqrt[3]{24 x}$

Step 1.2

Pull terms out from under the radical.

$- 9 (3 x \sqrt[3]{3 x}) - 5 x \sqrt[3]{24 x}$

Step 1.3

Multiply $3$ by $- 9$ .

$- 27 (x \sqrt[3]{3 x}) - 5 x \sqrt[3]{24 x}$

Step 1.4

Rewrite $24 x$ as $2^{3} \cdot (3 x)$ .

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Step 1.4.1

Factor $8$ out of $24$ .

$- 27 x \sqrt[3]{3 x} - 5 x \sqrt[3]{8 (3) x}$

Step 1.4.2

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

$- 27 x \sqrt[3]{3 x} - 5 x \sqrt[3]{2^{3} \cdot 3 x}$

Step 1.4.3

Add parentheses.

$- 27 x \sqrt[3]{3 x} - 5 x \sqrt[3]{2^{3} \cdot (3 x)}$

Step 1.5

Pull terms out from under the radical.

$- 27 x \sqrt[3]{3 x} - 5 x (2 \sqrt[3]{3 x})$

Step 1.6

Multiply $2$ by $- 5$ .

$- 27 x \sqrt[3]{3 x} - 10 x \sqrt[3]{3 x}$

Step 2

Subtract $10 x \sqrt[3]{3 x}$ from $- 27 x \sqrt[3]{3 x}$ .

$- 37 x \sqrt[3]{3 x}$