Evaluate each expression. See Example 5. 18 - 4² + 5 - (3 - 7)

Verified step by step guidance

1. Identify the order of operations to evaluate the expression: parentheses first, then exponents, followed by multiplication/division, and finally addition/subtraction.
2. Evaluate the expression inside the parentheses: calculate \((3 - 7)\).
3. Calculate the exponent: evaluate \$4^2$.
4. Substitute the results from steps 2 and 3 back into the expression, so it becomes \(18 - \text{(result of }4^2\text{)} + 5 - \text{(result of }3 - 7\text{)}\).
5. Perform the addition and subtraction from left to right to simplify the expression completely.

Key Concepts

Order of Operations (PEMDAS/BODMAS)

The order of operations dictates the sequence in which parts of a mathematical expression are evaluated: Parentheses first, then Exponents, followed by Multiplication and Division (left to right), and finally Addition and Subtraction (left to right). This ensures consistent and correct results.

Exponents

Exponents represent repeated multiplication of a base number. For example, 4² means 4 multiplied by itself once (4 × 4 = 16). Evaluating exponents before other operations is crucial to correctly simplifying expressions.

Simplifying Expressions with Parentheses

Parentheses indicate which parts of an expression should be evaluated first. Simplifying inside parentheses can change the overall value of the expression, so it is important to handle these sections carefully before proceeding with other operations.