Simplify 3 fourth root of 8*7 fourth root of 32

$3 \sqrt[4]{8} \cdot 7 \sqrt[4]{32}$

Step 1

Rewrite $32$ as $2^{4} \cdot 2$ .

Factor $16$ out of $32$ .

$3 \sqrt[4]{8} \cdot (7 \sqrt[4]{16 (2)})$

Rewrite $16$ as $2^{4}$ .

$3 \sqrt[4]{8} \cdot (7 \sqrt[4]{2^{4} \cdot 2})$

Step 2

Pull terms out from under the radical.

$3 \sqrt[4]{8} \cdot (7 (2 \sqrt[4]{2}))$

Step 3

Multiply $2$ by $7$ .

$3 \sqrt[4]{8} \cdot (14 \sqrt[4]{2})$

Step 4

Multiply $3 \sqrt[4]{8} (14 \sqrt[4]{2})$ .

Multiply $14$ by $3$ .

$42 \sqrt[4]{8} \sqrt[4]{2}$

Combine using the product rule for radicals.

$42 \sqrt[4]{2 \cdot 8}$

Multiply $2$ by $8$ .

$42 \sqrt[4]{16}$

Step 5

Rewrite $16$ as $2^{4}$ .

$42 \sqrt[4]{2^{4}}$

Step 6

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

$42 \cdot 2$

Step 7

Multiply $42$ by $2$ .

$84$