1. **State the problem:** Simplify the expression $$\frac{\sqrt[3]{121}+20-8}{5\times10-\frac{5^2}{5}}$$. 2. **Recall the rules and formulas:** - Cube root: $$\sqrt[3]{a}$$ is the number that when cubed gives $$a$$. - Order of operations: Calculate powers and roots first, then multiplication/division, and finally addition/subtraction. 3. **Calculate the cube root:** $$\sqrt[3]{121}$$ is approximately $$4.946$$ (since $$4.946^3 \approx 121$$). 4. **Simplify the numerator:** $$4.946 + 20 - 8 = 16.946$$. 5. **Simplify the denominator:** Calculate $$5 \times 10 = 50$$. Calculate $$5^2 = 25$$. Calculate $$\frac{25}{5} = 5$$. So denominator is $$50 - 5 = 45$$. 6. **Divide numerator by denominator:** $$\frac{16.946}{45} \approx 0.3766$$. **Final answer:** $$\approx 0.377$$ (rounded to three decimal places).