Simplify 3 fourth root of 32*(-6 fourth root of 5)

$3 \sqrt[4]{32} \cdot (- 6 \sqrt[4]{5})$

Step 1

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

Factor $16$ out of $32$ .

$3 \sqrt[4]{16 (2)} \cdot (- 6 \sqrt[4]{5})$

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

$3 \sqrt[4]{2^{4} \cdot 2} \cdot (- 6 \sqrt[4]{5})$

Step 2

Pull terms out from under the radical.

$3 (2 \sqrt[4]{2}) \cdot (- 6 \sqrt[4]{5})$

Step 3

Multiply $2$ by $3$ .

$6 \sqrt[4]{2} \cdot (- 6 \sqrt[4]{5})$

Step 4

Multiply $6 \sqrt[4]{2} (- 6 \sqrt[4]{5})$ .

Multiply $- 6$ by $6$ .

$- 36 \sqrt[4]{2} \sqrt[4]{5}$

Combine using the product rule for radicals.

$- 36 \sqrt[4]{5 \cdot 2}$

Multiply $5$ by $2$ .

$- 36 \sqrt[4]{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- 36 \sqrt[4]{10}$

Decimal Form:

$- 64.01805876 \dots$