Simplify 7 cube root of 16* cube root of 8

$7 \sqrt[3]{16} \cdot \sqrt[3]{8}$

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

Factor $8$ out of $16$ .

$7 \sqrt[3]{8 (2)} \cdot \sqrt[3]{8}$

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

$7 \sqrt[3]{2^{3} \cdot 2} \cdot \sqrt[3]{8}$

Pull terms out from under the radical.

$7 (2 \sqrt[3]{2}) \cdot \sqrt[3]{8}$

Write the expression using exponents.

Multiply $2$ by $7$ .

$14 \sqrt[3]{2} \cdot \sqrt[3]{8}$

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

$14 \sqrt[3]{2} \cdot \sqrt[3]{2^{3}}$

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

$14 \sqrt[3]{2} \cdot 2$

Multiply $2$ by $14$ .

$28 \sqrt[3]{2}$

The result can be shown in multiple forms.

Exact Form:

$28 \sqrt[3]{2}$

Decimal Form:

$35.27778939 \dots$