Algebra Examples

$4 \sqrt[3]{- 9} \cdot 7 \sqrt[3]{48}$

Step 1

Rewrite $- 9$ as ${(- 1)}^{3} \cdot 9$ .

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Step 1.1

Rewrite $- 9$ as $- 1 (9)$ .

$4 \sqrt[3]{- 1 (9)} \cdot (7 \sqrt[3]{48})$

Step 1.2

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$4 \sqrt[3]{{(- 1)}^{3} \cdot 9} \cdot (7 \sqrt[3]{48})$

$4 \sqrt[3]{{(- 1)}^{3} \cdot 9} \cdot (7 \sqrt[3]{48})$

Step 2

Pull terms out from under the radical.

$4 (- 1 \sqrt[3]{9}) \cdot (7 \sqrt[3]{48})$

Step 3

Simplify the expression.

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Step 3.1

Rewrite $- 1 \sqrt[3]{9}$ as $- \sqrt[3]{9}$ .

$4 (- \sqrt[3]{9}) \cdot (7 \sqrt[3]{48})$

Step 3.2

Multiply $- 1$ by $4$ .

$- 4 \sqrt[3]{9} \cdot (7 \sqrt[3]{48})$

$- 4 \sqrt[3]{9} \cdot (7 \sqrt[3]{48})$

Step 4

Rewrite $48$ as $2^{3} \cdot 6$ .

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Step 4.1

Factor $8$ out of $48$ .

$- 4 \sqrt[3]{9} \cdot (7 \sqrt[3]{8 (6)})$

Step 4.2

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

$- 4 \sqrt[3]{9} \cdot (7 \sqrt[3]{2^{3} \cdot 6})$

$- 4 \sqrt[3]{9} \cdot (7 \sqrt[3]{2^{3} \cdot 6})$

Step 5

Pull terms out from under the radical.

$- 4 \sqrt[3]{9} \cdot (7 (2 \sqrt[3]{6}))$

Step 6

Multiply $2$ by $7$ .

$- 4 \sqrt[3]{9} \cdot (14 \sqrt[3]{6})$

Step 7

Multiply $- 4 \sqrt[3]{9} (14 \sqrt[3]{6})$ .

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Step 7.1

Multiply $14$ by $- 4$ .

$- 56 \sqrt[3]{9} \sqrt[3]{6}$

Step 7.2

Combine using the product rule for radicals.

$- 56 \sqrt[3]{6 \cdot 9}$

Step 7.3

Multiply $6$ by $9$ .

$- 56 \sqrt[3]{54}$

$- 56 \sqrt[3]{54}$

Step 8

Rewrite $54$ as $3^{3} \cdot 2$ .

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Step 8.1

Factor $27$ out of $54$ .

$- 56 \sqrt[3]{27 (2)}$

Step 8.2

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

$- 56 \sqrt[3]{3^{3} \cdot 2}$

$- 56 \sqrt[3]{3^{3} \cdot 2}$

Step 9

Pull terms out from under the radical.

$- 56 (3 \sqrt[3]{2})$

Step 10

Multiply $3$ by $- 56$ .

$- 168 \sqrt[3]{2}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$- 168 \sqrt[3]{2}$

Decimal Form:

$- 211.66673638 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$