Simplify cube root of 54x^3- cube root of 16x^3

$\sqrt[3]{54 x^{3}} - \sqrt[3]{16 x^{3}}$

Step 1

Simplify each term.

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

Factor $27$ out of $54$ .

$\sqrt[3]{27 (2) x^{3}} - \sqrt[3]{16 x^{3}}$

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

$\sqrt[3]{3^{3} \cdot 2 x^{3}} - \sqrt[3]{16 x^{3}}$

Move $2$ .

$\sqrt[3]{3^{3} x^{3} \cdot 2} - \sqrt[3]{16 x^{3}}$

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

$\sqrt[3]{{(3 x)}^{3} \cdot 2} - \sqrt[3]{16 x^{3}}$

Pull terms out from under the radical.

$3 x \sqrt[3]{2} - \sqrt[3]{16 x^{3}}$

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

Factor $8$ out of $16$ .

$3 x \sqrt[3]{2} - \sqrt[3]{8 (2) x^{3}}$

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

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

Move $2$ .

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

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 1$ .

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

Step 2

Simplify by adding terms.

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

$1 x \sqrt[3]{2}$

Multiply $x$ by $1$ .

$x \sqrt[3]{2}$