ITPEC FE Subject A April 2026 Question 1

Topic: Basic Theory

Which of the following is the prefix notation for the infix expression ((a−b)/(c+d))^e . Here, the symbols “+,” “−,” “/,” and “^” represent addition, subtraction, division, and exponentiation operators, respectively.

a)^e/+dc−bab)^−ab/+cdec)^/−ab+cded)^e/−ab+cd

Explanation

^/−ab+cde — in prefix notation every operator is written before its two operands, so convert from the innermost parentheses outward.

Treat each converted group as a single operand:

•a−b → −ab
•c+d → +cd
•(a−b)/(c+d) → /−ab+cd
•that quotient raised to e → ^/−ab+cde

Answer (c)

Why not others:

•(a) ^e/+dc−ba — the postfix form ab−cd+/e^ written backwards; reversing postfix also reverses every operand pair
•(b) ^−ab/+cde — reads as a−b raised to (c+d)/e, so the division has moved into the exponent
•(d) ^e/−ab+cd — puts e first, making e the base and the quotient the exponent

Key rule: Converting between infix, prefix and postfix changes only where the operators sit; the operands keep their left-to-right order.

Basic Theory · AI-written, may contain errors

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