1. **State the problem:** Convert the postfix expression $$A B * C D ^ / E F G + * + H I + J K - / -$$ to its equivalent infix form, then evaluate it using values $$A=100, B=10, C=2, D=3, E=15, F=4, G=6, H=24, I=26, J=15, K=5$$. 2. **Convert postfix to infix step-by-step:** - Push operands onto a stack. - When an operator appears, pop operands needed, form infix with parentheses, push back. Stack operations by tokens: - A: push A - B: push B - *: pop B and A, push (A * B) - C: push C - D: push D - ^: pop D and C, push (C ^ D) - /: pop (C ^ D) and (A * B), push ((A * B) / (C ^ D)) - E: push E - F: push F - G: push G - +: pop G and F, push (F + G) - *: pop (F + G) and E, push (E * (F + G)) - +: pop (E * (F + G)) and ((A * B) / (C ^ D)), push (((A * B) / (C ^ D)) + (E * (F + G))) - H: push H - I: push I - +: pop I and H, push (H + I) - J: push J - K: push K - -: pop K and J, push (J - K) - /: pop (J - K) and (H + I), push ((H + I) / (J - K)) - -: pop ((H + I) / (J - K)) and (((A * B) / (C ^ D)) + (E * (F + G))), push final: $$(((A * B) / (C ^ D)) + (E * (F + G))) - ((H + I) / (J - K))$$ 3. **Final infix expression:** $$(((A * B) / (C ^ D)) + (E * (F + G))) - ((H + I) / (J - K))$$ 4. **Evaluate the expression with given values:** - Calculate powers: $$C^D = 2^3 = 8$$ - Multiply: $$A * B = 100 * 10 = 1000$$ - Divide: $$\frac{1000}{8} = 125$$ - Sum inside second parenthesis: $$F + G = 4 + 6 = 10$$ - Multiply: $$E * 10 = 15 * 10 = 150$$ - Sum: $$125 + 150 = 275$$ - Sum: $$H + I = 24 + 26 = 50$$ - Subtract: $$J - K = 15 - 5 = 10$$ - Divide: $$\frac{50}{10} = 5$$ - Final subtraction: $$275 - 5 = 270$$ **Answer:** The evaluated value of the postfix expression with given values is $$270$$.