Simplify 5 cube root of 64x^7-x cube root of 8x^4

$5 \sqrt[3]{64 x^{7}} - x \sqrt[3]{8 x^{4}}$

Step 1

Simplify each term.

Rewrite $64 x^{7}$ as ${(4 x^{2})}^{3} x$ .

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

$5 \sqrt[3]{4^{3} x^{7}} - x \sqrt[3]{8 x^{4}}$

Factor out $x^{6}$ .

$5 \sqrt[3]{4^{3} (x^{6} x)} - x \sqrt[3]{8 x^{4}}$

Rewrite $x^{6}$ as ${(x^{2})}^{3}$ .

$5 \sqrt[3]{4^{3} ({(x^{2})}^{3} x)} - x \sqrt[3]{8 x^{4}}$

Rewrite $4^{3} {(x^{2})}^{3}$ as ${(4 x^{2})}^{3}$ .

$5 \sqrt[3]{{(4 x^{2})}^{3} x} - x \sqrt[3]{8 x^{4}}$

Pull terms out from under the radical.

$5 (4 x^{2} \sqrt[3]{x}) - x \sqrt[3]{8 x^{4}}$

Multiply $4$ by $5$ .

$20 (x^{2} \sqrt[3]{x}) - x \sqrt[3]{8 x^{4}}$

Rewrite $8 x^{4}$ as ${(2 x)}^{3} x$ .

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

$20 x^{2} \sqrt[3]{x} - x \sqrt[3]{2^{3} x^{4}}$

Factor out $x^{3}$ .

$20 x^{2} \sqrt[3]{x} - x \sqrt[3]{2^{3} (x^{3} x)}$

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

$20 x^{2} \sqrt[3]{x} - x \sqrt[3]{{(2 x)}^{3} x}$

Pull terms out from under the radical.

$20 x^{2} \sqrt[3]{x} - x (2 x \sqrt[3]{x})$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$20 x^{2} \sqrt[3]{x} - (x \cdot x) (2 \sqrt[3]{x})$

Multiply $x$ by $x$ .

$20 x^{2} \sqrt[3]{x} - x^{2} (2 \sqrt[3]{x})$

Multiply $2$ by $- 1$ .

$20 x^{2} \sqrt[3]{x} - 2 x^{2} \sqrt[3]{x}$

Step 2

Subtract $2 x^{2} \sqrt[3]{x}$ from $20 x^{2} \sqrt[3]{x}$ .

$18 x^{2} \sqrt[3]{x}$