Simplify cube root of 8x^2* square root of 16x^6

$\sqrt[3]{8 x^{2}} \cdot \sqrt{16 x^{6}}$

Step 1

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

$\sqrt[3]{2^{3} x^{2}} \cdot \sqrt{16 x^{6}}$

Step 2

Pull terms out from under the radical.

$2 \sqrt[3]{x^{2}} \cdot \sqrt{16 x^{6}}$

Step 3

Rewrite $16 x^{6}$ as ${(4 x^{3})}^{2}$ .

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

Step 4

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

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

Step 5

Multiply $4$ by $2$ .

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