Simplify cube root of 24x- cube root of 192x

$\sqrt[3]{24 x} - \sqrt[3]{192 x}$

Step 1

Simplify each term.

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

Factor $8$ out of $24$ .

$\sqrt[3]{8 (3) x} - \sqrt[3]{192 x}$

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

$\sqrt[3]{2^{3} \cdot 3 x} - \sqrt[3]{192 x}$

Add parentheses.

$\sqrt[3]{2^{3} \cdot (3 x)} - \sqrt[3]{192 x}$

Pull terms out from under the radical.

$2 \sqrt[3]{3 x} - \sqrt[3]{192 x}$

Rewrite $192 x$ as $4^{3} \cdot (3 x)$ .

Factor $64$ out of $192$ .

$2 \sqrt[3]{3 x} - \sqrt[3]{64 (3) x}$

Rewrite $64$ as $4^{3}$ .

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $4$ by $- 1$ .

$2 \sqrt[3]{3 x} - 4 \sqrt[3]{3 x}$

Step 2

Subtract $4 \sqrt[3]{3 x}$ from $2 \sqrt[3]{3 x}$ .

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