Simplify cube root of 2x^2* cube root of 4x

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

Step 1

Multiply $\sqrt[3]{2 x^{2}} \sqrt[3]{4 x}$ .

Combine using the product rule for radicals.

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

Multiply $4$ by $2$ .

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

Raise $x$ to the power of $1$ .

$\sqrt[3]{8 (x^{1} x^{2})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt[3]{8 x^{1 + 2}}$

Add $1$ and $2$ .

$\sqrt[3]{8 x^{3}}$

Step 2

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

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

Step 3

Pull terms out from under the radical, assuming real numbers.

$2 x$