Final Answer:
The binary tree representation of the arithmetic expression is complex to describe textually due to formatting limitations. However, if you draw it, the tree structure would contain nodes representing each operator (+, -, *, /) and operands (5, 2, 1, 9, 7, 2, 8), arranged hierarchically according to the order of operations.
Step-by-step explanation:
The expression contains arithmetic operations within parentheses, indicating the precedence of calculations. To illustrate this in a binary tree format, we'll start with the main operations and build the tree outward. For instance, the innermost parentheses, (2−1), form a subtree with the subtraction operator at the root and operands 2 and 1 as its children. Similarly, other inner expressions build substructures following the operator precedence rules.
Next, we'd branch out to create subtrees for higher-order operations like addition, subtraction, multiplication, and division. For instance, the addition of 5 and 2 forms a subtree under the addition operator, and the subtraction of 7 and 2 within parentheses also generates its subtree. These subtrees then become children of the division operator subtree.
Continuing this process, we construct the entire binary tree by arranging these subtrees in accordance with the mathematical operations' hierarchical order. Each node represents an operation, and the leaf nodes represent the operands. Ultimately, the fully drawn binary tree accurately depicts the structural organization of the arithmetic expression.