Simplify ( cube root of 16- cube root of 54)/( cube root of 2)

$\frac{\sqrt[3]{16} - \sqrt[3]{54}}{\sqrt[3]{2}}$

Simplify the numerator.

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

Factor $8$ out of $16$ .

$\frac{\sqrt[3]{8 (2)} - \sqrt[3]{54}}{\sqrt[3]{2}}$

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

$\frac{\sqrt[3]{2^{3} \cdot 2} - \sqrt[3]{54}}{\sqrt[3]{2}}$

Pull terms out from under the radical.

$\frac{2 \sqrt[3]{2} - \sqrt[3]{54}}{\sqrt[3]{2}}$

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

Factor $27$ out of $54$ .

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

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

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

Pull terms out from under the radical.

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

Multiply $3$ by $- 1$ .

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

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

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

Cancel the common factor of $\sqrt[3]{2}$ .

Cancel the common factor.

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

Divide $- 1$ by $1$ .

$- 1$