Simplify the Radical Expression 4 cube root of -9*7 cube root of 48

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

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

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

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

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

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

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

Pull terms out from under the radical.

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

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

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

Multiply $- 1$ by $4$ .

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

Multiply $7$ by $- 4$ .

$- 28 \sqrt[3]{9} \sqrt[3]{48}$

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

Factor $8$ out of $48$ .

$- 28 \sqrt[3]{9} \sqrt[3]{8 (6)}$

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

$- 28 \sqrt[3]{9} \sqrt[3]{2^{3} \cdot 6}$

$- 28 \sqrt[3]{9} \sqrt[3]{2^{3} \cdot 6}$

Pull terms out from under the radical.

$- 28 \sqrt[3]{9} (2 \sqrt[3]{6})$

Multiply $- 28 \sqrt[3]{9} (2 \sqrt[3]{6})$ .

Multiply $2$ by $- 28$ .

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

Combine using the product rule for radicals.

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

Multiply $6$ by $9$ .

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

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

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

Factor $27$ out of $54$ .

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

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

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

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

Pull terms out from under the radical.

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

Multiply $3$ by $- 56$ .

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 211.66673638 \dots$

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