lesson
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If two people solve 3+2×42, one person gets 80 and the other gets 35. Only one answer is mathematically correct.
Without agreed-upon rules, math would be chaos because different orders give completely different numbers.
The Priority Ladder
The order of operations is the standard rulebook that tells us which operation to calculate first: PEMDAS.
An exponent represents repeated multiplication, like 42=4×4, which is why exponents must be evaluated before any surrounding multiplication or addition.
📊A clean vertical step-ladder infographic showing the PEMDAS hierarchy. Top rung: '1. Parentheses ( )' in purple (#8b5cf6). Second rung: '2. Exponents x²' in blue (#2563eb) highlighted with a glow. Third rung: '3. Multiply & Divide (Left to Right)' in teal (#0d9488). Bottom rung: '4. Add & Subtract (Left to Right)' in amber (#d97706). On the right side, an example badge shows '3 + 2 × 4² = 3 + 2 × 16 = 3 + 32 = 35'. Minimal card style, light background (#f8fafc), dark text (#1e293b), rounded corners.
What does this look like step-by-step when an expression mixes exponents with other operations?
Step-by-Step Evaluation
Let's evaluate 6+3×23−5. First, find the power: 23 means 2×2×2=8.
Next, multiply 3×8=24, giving 6+24−5. Finally, add and subtract from left to right: 30−5=25.
📊A step-by-step math evaluation visual for '6 + 3 × 2³ - 5'. Card 1 (Top): Original expression with '2³' highlighted in blue. An arrow points down showing '2³ = 8'. Card 2: '6 + 3 × 8 - 5' with '3 × 8' highlighted in teal. An arrow points down showing '3 × 8 = 24'. Card 3: '6 + 24 - 5' with '6 + 24' highlighted in amber. Card 4: '30 - 5 = 25' in a bold green success box. Clean minimal design with downward arrows linking each line.
What happens when grouping symbols like parentheses enter the picture?