1. The problem is to evaluate the expression $$\sqrt[4]{81y^{8}x^{4}}$$. 2. Recall the rule for radicals: $$\sqrt[n]{a^{m}} = a^{\frac{m}{n}}$$. This means the fourth root of a power is the power raised to the one-fourth. 3. Apply the fourth root to each factor inside the radical separately: $$\sqrt[4]{81} \times \sqrt[4]{y^{8}} \times \sqrt[4]{x^{4}}$$. 4. Simplify each term: - $$\sqrt[4]{81} = 81^{\frac{1}{4}} = (3^{4})^{\frac{1}{4}} = 3$$ - $$\sqrt[4]{y^{8}} = y^{\frac{8}{4}} = y^{2}$$ - $$\sqrt[4]{x^{4}} = x^{\frac{4}{4}} = x^{1} = x$$ 5. Multiply the simplified terms: $$3 \times y^{2} \times x = 3y^{2}x$$ 6. Therefore, the evaluated expression is $$3y^{2}x$$. This matches the second answer choice.