Use the product rule to multiply the following.
$\sqrt[4]{7m^2}\cdot \sqrt[4]{2n}$

• A. $\(\sqrt\)[4]{7m^2+2n}$
• B. $\(\sqrt\)[4]{14m^2n}$
• C. $\(\left\)(\(\sqrt\)[4]{14m^2}\(\right\))n$
• D. $\(\sqrt\)[4]{7m^2}+\(\sqrt\)[4]{2n}$

Answer: (B)

Verified step by step guidance

1. Identify the expression to multiply: \(\sqrt[4]{7m^{2}} \cdot \sqrt[4]{2n}\).
2. Recall the product rule for radicals with the same index: \(\sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{a \cdot b}\).
3. Apply the product rule by multiplying the radicands (the expressions inside the roots): \(7m^{2} \times 2n = 14m^{2}n\).
4. Rewrite the product under a single fourth root: \(\sqrt[4]{14m^{2}n}\).
5. This expression represents the simplified product of the original radicals using the product rule.