Goal
We want to evaluate the expression:
(72 ÷ 12 × 5)² − 18 × 3²
Step 1: Understand the order of operations
Remember the acronym PEMDAS/BODMAS:
- P/B: Parentheses/Brackets first
- E/O: Exponents/Orders (squares, square roots, etc.)
- MD/DM: Multiplication and Division from left to right
- AS/S: Addition and Subtraction from left to right
Step 2: Solve inside the parentheses (72 ÷ 12 × 5)
Do division and multiplication from left to right:
- 72 ÷ 12 = 6
- 6 × 5 = 30
So, (72 ÷ 12 × 5) = 30
Step 3: Apply the exponent to the result inside the parentheses
(72 ÷ 12 × 5)² = 30² = 900
Step 4: Solve the second part: 18 × 3²
First compute 3² = 9
Then multiply by 18: 18 × 9 = 162
Step 5: Subtract the second part from the first part
900 − 162 = 738
Final answer
The value of the expression is 738.