Simplify 8 cube root of a^4b^3c^2-14ab cube root of ac^2

$8 \sqrt[3]{a^{4} b^{3} c^{2}} - 14 a b \sqrt[3]{a c^{2}}$

Step 1

Simplify each term.

Rewrite $a^{4} b^{3} c^{2}$ as ${(a b)}^{3} (a c^{2})$ .

Factor out $a^{3}$ .

$8 \sqrt[3]{a^{3} a b^{3} c^{2}} - 14 a b \sqrt[3]{a c^{2}}$

Move $a$ .

$8 \sqrt[3]{a^{3} b^{3} a c^{2}} - 14 a b \sqrt[3]{a c^{2}}$

Rewrite $a^{3} b^{3}$ as ${(a b)}^{3}$ .

$8 \sqrt[3]{{(a b)}^{3} a c^{2}} - 14 a b \sqrt[3]{a c^{2}}$

Add parentheses.

$8 \sqrt[3]{{(a b)}^{3} (a c^{2})} - 14 a b \sqrt[3]{a c^{2}}$

Pull terms out from under the radical.

$8 a b \sqrt[3]{a c^{2}} - 14 a b \sqrt[3]{a c^{2}}$

Step 2

Subtract $14 a b \sqrt[3]{a c^{2}}$ from $8 a b \sqrt[3]{a c^{2}}$ .

$- 6 a b \sqrt[3]{a c^{2}}$