1. The problem is to simplify the expression $$\sqrt[3]{\frac{80}{000}} \div \left(7.1 + \sqrt[3]{12,180} + 12,209\right).$$ 2. First, note that the expression $$\frac{80}{000}$$ is ambiguous because "000" is not a valid number. Assuming it means 80 divided by 1000, rewrite as $$\frac{80}{1000} = 0.08$$. 3. Calculate the cube root of 0.08: $$\sqrt[3]{0.08} = \sqrt[3]{\frac{8}{100}} = \frac{\sqrt[3]{8}}{\sqrt[3]{100}} = \frac{2}{\sqrt[3]{100}}.$$ Since $$\sqrt[3]{100} = 100^{1/3} \approx 4.6416,$$ then $$\sqrt[3]{0.08} \approx \frac{2}{4.6416} \approx 0.431.$$ 4. Next, calculate $$\sqrt[3]{12,180}$$. Assuming the comma is a thousands separator, this is $$\sqrt[3]{12180}$$. 5. Approximate $$\sqrt[3]{12180}$$: Since $$22^3 = 10648$$ and $$23^3 = 12167$$, and $$24^3 = 13824$$, the cube root is about 23. 6. Now sum the terms inside the parentheses: $$7.1 + 23 + 12209 = 7.1 + 23 + 12209 = 12239.1.$$ 7. Finally, divide the cube root of 0.08 by this sum: $$\frac{0.431}{12239.1} \approx 3.52 \times 10^{-5}.$$ **Final answer:** $$\approx 3.52 \times 10^{-5}.$$