1. **State the problem:** Simplify the expression $$\sqrt[5]{\frac{3^{12} \times 2^{10}}{3^2}}$$. 2. **Use the properties of exponents:** When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Simplify inside the radical:** $$\frac{3^{12} \times 2^{10}}{3^2} = 3^{12-2} \times 2^{10} = 3^{10} \times 2^{10}$$. 4. **Rewrite the expression:** $$\sqrt[5]{3^{10} \times 2^{10}} = \sqrt[5]{(3^{10})(2^{10})}$$. 5. **Use the property of radicals:** $$\sqrt[5]{a^m} = a^{\frac{m}{5}}$$. 6. **Apply the property:** $$\sqrt[5]{3^{10} \times 2^{10}} = 3^{\frac{10}{5}} \times 2^{\frac{10}{5}} = 3^2 \times 2^2$$. 7. **Calculate the powers:** $$3^2 = 9, \quad 2^2 = 4$$. 8. **Multiply the results:** $$9 \times 4 = 36$$. **Final answer:** $$36$$