Simplify cube root of 16* cube root of 8

$\sqrt[3]{16} \cdot \sqrt[3]{8}$

Step 1

Rewrite $16$ as $2^{3} \cdot 2$ .

Factor $8$ out of $16$ .

$\sqrt[3]{8 (2)} \cdot \sqrt[3]{8}$

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

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

Step 2

Pull terms out from under the radical.

$2 \sqrt[3]{2} \cdot \sqrt[3]{8}$

Step 3

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

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

Step 4

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

$2 \sqrt[3]{2} \cdot 2$

Step 5

Multiply $2$ by $2$ .

$4 \sqrt[3]{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt[3]{2}$

Decimal Form:

$5.03968419 \dots$