1. **State the problem:** Simplify the expression $$\sqrt[5]{64x^{9}y^{4}}$$. 2. **Recall the rule for radicals:** $$\sqrt[n]{a^{m}} = a^{\frac{m}{n}}$$. 3. **Rewrite each part inside the radical using fractional exponents:** $$\sqrt[5]{64} = 64^{\frac{1}{5}}, \quad \sqrt[5]{x^{9}} = x^{\frac{9}{5}}, \quad \sqrt[5]{y^{4}} = y^{\frac{4}{5}}$$ 4. **Simplify the constant:** $$64 = 2^{6} \implies 64^{\frac{1}{5}} = 2^{\frac{6}{5}} = 2^{1 + \frac{1}{5}} = 2 \cdot 2^{\frac{1}{5}}$$ 5. **Rewrite the variables:** $$x^{\frac{9}{5}} = x^{1 + \frac{4}{5}} = x \cdot x^{\frac{4}{5}}, \quad y^{\frac{4}{5}} \text{ stays as is}$$ 6. **Combine all parts:** $$\sqrt[5]{64x^{9}y^{4}} = 2 \cdot 2^{\frac{1}{5}} \cdot x \cdot x^{\frac{4}{5}} \cdot y^{\frac{4}{5}} = 2x \cdot \sqrt[5]{2x^{4}y^{4}}$$ 7. **Express the remaining radical:** $$\sqrt[5]{2x^{4}y^{4}} = \sqrt[5]{2xy^{4} \cdot x^{3}} = \sqrt[5]{2xy^{4}} \cdot \sqrt[5]{x^{3}}$$ but since we want simplest form, keep as $$\sqrt[5]{2x^{4}y^{4}}$$ or equivalently $$\sqrt[5]{2xy^{4} \cdot x^{3}}$$. 8. **Match with given options:** Option (c) is $$2x \sqrt[3]{2xy^{4}}$$ but the root is cube root, not fifth root. Option (a) is $$2 \sqrt[3]{2x^{2}y^{4}}$$ also cube root. Option (b) is $$2x \sqrt[3]{2xy}$$ cube root. Option (d) is $$\sqrt[5]{61x^{5}y^{-1}}$$ different number and powers. Option (e) None of the above. Since the simplified form is $$2x \sqrt[5]{2x^{4}y^{4}}$$ and none of the options match exactly, the answer is (e) None of the above.