Simplify cube root of 81x^4- cube root of 24x

$\sqrt[3]{81 x^{4}} - \sqrt[3]{24 x}$

Step 1

Rewrite $81 x^{4}$ as ${(3 x)}^{3} \cdot (3 x)$ .

Factor $27$ out of $81$ .

$\sqrt[3]{27 (3) x^{4}} - \sqrt[3]{24 x}$

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

$\sqrt[3]{3^{3} \cdot 3 x^{4}} - \sqrt[3]{24 x}$

Factor out $x^{3}$ .

$\sqrt[3]{3^{3} \cdot 3 (x^{3} x)} - \sqrt[3]{24 x}$

Move $3$ .

$\sqrt[3]{3^{3} x^{3} \cdot 3 x} - \sqrt[3]{24 x}$

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

$\sqrt[3]{{(3 x)}^{3} \cdot 3 x} - \sqrt[3]{24 x}$

Add parentheses.

$\sqrt[3]{{(3 x)}^{3} \cdot (3 x)} - \sqrt[3]{24 x}$

Step 2

Pull terms out from under the radical.

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

Step 3

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

Factor $8$ out of $24$ .

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

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

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

Add parentheses.

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

Step 4

Pull terms out from under the radical.

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

Step 5

Multiply $2$ by $- 1$ .

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