In expression conversion, convert the following infix expression to its equivalent prefix notation: ((A + B) * C – (D – E) ^ (F + G))

Introduction / Context:
This question checks your understanding of operator precedence and associativity as well as your ability to convert an infix arithmetic expression to prefix notation. Prefix expressions place operators before their operands and remove the need for parentheses when precedence and associativity are handled correctly.

Given Data / Assumptions:

The given infix expression is ((A + B) * C – (D – E) ^ (F + G)).
The operator precedence is assumed as follows: exponentiation has the highest precedence, then multiplication, then addition and subtraction.
The caret symbol is used to denote exponentiation.
Subtraction and addition are left associative, while exponentiation is usually treated as right associative.

Concept / Approach:
To convert an infix expression to prefix form, you can either construct an expression tree and then perform a preorder traversal, or use a stack based algorithm. The key is to respect operator precedence and explicit parentheses. The expression here can be grouped as (A + B) * C for the left part and (D – E) ^ (F + G) for the right part. The whole expression is then left part minus right part.

Step-by-Step Solution:
Start with the innermost parenthesized subexpressions: A + B and D – E and F + G. Convert A + B to prefix: + A B. Multiply this result by C, giving the infix group (A + B) * C, which in prefix is * (+ A B) C or * + A B C. For the right side, convert D – E to prefix: - D E, and F + G to prefix: + F G. Apply exponentiation on these two prefix expressions to get ^ - D E + F G. Finally, subtract the right side from the left side: (left) – (right) becomes prefix - (left) (right), which yields - * + A B C ^ - D E + F G.

Verification / Alternative check:
You can verify correctness by building a tree with the top node as minus, left child as the multiplication of (A + B) and C, and right child as exponentiation of (D – E) by (F + G). Performing a preorder traversal (visit root, then left subtree, then right subtree) produces the sequence - * + A B C ^ - D E + F G. None of the other options correspond to this tree structure.

Why Other Options Are Wrong:
Option b incorrectly makes multiplication the outermost operator and does not respect the top level subtraction.
Option c incorrectly places the subtraction around addition and multiplication in the wrong order.
Option d places exponentiation at the top, which does not match the original top level minus in the infix expression.

Common Pitfalls:
Learners often confuse the order in which to apply operators when converting complex expressions. Forgetting to group subexpressions correctly or ignoring operator precedence leads to incorrect trees and wrong prefix forms. A reliable method is to first fully parenthesize the infix expression, then carefully convert each group in a systematic manner.

Final Answer:
The correct prefix notation for the expression is - * + A B C ^ - D E + F G.