1. **Stating the problem:** Simplify the expression $$25.23: 1(2+3.2): 5+123.3.5+(3.22)_{(2.3.5)}:6:3-122:3:4$$. 2. **Clarify notation and operations:** Here, ":" denotes division, parentheses indicate multiplication or grouping, and underscores likely indicate grouping or subscript notation. We interpret the expression step-by-step. 3. **Calculate inside parentheses:** - $$2+3.2 = 2 + 3 \times 2 = 2 + 6 = 8$$ - $$3.22 = 3 \times 22 = 66$$ - $$2.3.5 = 2 \times 3 \times 5 = 30$$ 4. **Rewrite expression with calculated values:** $$25.23 : 1 \times 8 : 5 + 123.3.5 + 66_{30} : 6 : 3 - 122 : 3 : 4$$ 5. **Calculate multiplications:** - $$25.23 = 25 \times 23 = 575$$ - $$123.3.5 = 123 \times 3 \times 5 = 1845$$ 6. **Interpret $$66_{30}$$ as $$66 : 30$$ (division): $$66 : 30 = \frac{66}{30} = \frac{11}{5}$$ 7. **Rewrite expression:** $$575 : 1 \times 8 : 5 + 1845 + \frac{11}{5} : 6 : 3 - 122 : 3 : 4$$ 8. **Simplify divisions and multiplications from left to right:** - $$575 : 1 = 575$$ - $$575 \times 8 = 4600$$ - $$4600 : 5 = 920$$ 9. **Simplify the fraction chain:** - $$\frac{11}{5} : 6 = \frac{11}{5} \times \frac{1}{6} = \frac{11}{30}$$ - $$\frac{11}{30} : 3 = \frac{11}{30} \times \frac{1}{3} = \frac{11}{90}$$ 10. **Simplify the last division chain:** - $$122 : 3 = \frac{122}{3}$$ - $$\frac{122}{3} : 4 = \frac{122}{3} \times \frac{1}{4} = \frac{122}{12} = \frac{61}{6}$$ 11. **Rewrite expression:** $$920 + 1845 + \frac{11}{90} - \frac{61}{6}$$ 12. **Find common denominator for fractions:** - Common denominator is 90. - $$\frac{61}{6} = \frac{61 \times 15}{6 \times 15} = \frac{915}{90}$$ 13. **Combine fractions:** $$\frac{11}{90} - \frac{915}{90} = \frac{11 - 915}{90} = \frac{-904}{90} = -\frac{452}{45}$$ 14. **Add whole numbers and fraction:** $$920 + 1845 - \frac{452}{45} = 2765 - \frac{452}{45} = \frac{2765 \times 45}{45} - \frac{452}{45} = \frac{124425 - 452}{45} = \frac{123973}{45}$$ 15. **Final simplified result:** $$\boxed{\frac{123973}{45} \approx 2754.96}$$