Simplify -3 fourth root of 10*3 fourth root of 500

$- 3 \sqrt[4]{10} \cdot 3 \sqrt[4]{500}$

Multiply $- 3 \sqrt[4]{10} (3 \sqrt[4]{500})$ .

Multiply $3$ by $- 3$ .

$- 9 \sqrt[4]{10} \sqrt[4]{500}$

Combine using the product rule for radicals.

$- 9 \sqrt[4]{500 \cdot 10}$

Multiply $500$ by $10$ .

$- 9 \sqrt[4]{5000}$

$- 9 \sqrt[4]{5000}$

Rewrite $5000$ as $5^{4} \cdot 8$ .

Factor $625$ out of $5000$ .

$- 9 \sqrt[4]{625 (8)}$

Rewrite $625$ as $5^{4}$ .

$- 9 \sqrt[4]{5^{4} \cdot 8}$

$- 9 \sqrt[4]{5^{4} \cdot 8}$

Pull terms out from under the radical.

$- 9 (5 \sqrt[4]{8})$

Multiply $5$ by $- 9$ .

$- 45 \sqrt[4]{8}$

The result can be shown in multiple forms.

Exact Form:

$- 45 \sqrt[4]{8}$

Decimal Form:

$- 75.68067737 \dots$

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