🧱 See It
Brackets, then Exponents, then Divide/Multiply, then Add/Subtract — the "E" has been missing this whole time, waiting for exponents to be introduced. Now it takes its place, and BEDMAS is finally the complete rule. The numbers themselves can now be anything: whole, negative, decimal, or fraction — the order never changes.
✏️ Draw It
Number the operations in order before calculating anything, exactly like always:
4
④
+
(6 − 2)
①
²
③
÷
8
Brackets ①, exponent ②, divide ③, add ④ — the exponent step happens right after brackets, before any multiplying or dividing.
🔢 Write It
4 + (6 − 2)² ÷ 8
- Brackets:
6 − 2 = 4 - Exponent:
4² = 16 - Divide:
16 ÷ 8 = 2 - Add:
4 + 2 = 6
If the base being squared is negative, resolve the brackets around it FIRST, then square the result — never square just part of a bracketed expression.
💡 Worked Examples
Example 1: −2 × (3 − 5)² + 7
- Brackets:
3 − 5 = −2 - Exponent:
(−2)² = 4(squaring a negative gives a positive) - Multiply:
−2 × 4 = −8 - Add:
−8 + 7 = −1 - Answer:
−1
Example 2: 3 + 2 × (1/2)²
- Brackets: already simplified,
1/2 - Exponent:
(1/2)² = 1/4 - Multiply:
2 × 1/4 = 1/2 - Add:
3 + 1/2 = 3 1/2 - Answer:
3 1/2
🧠 Quick Reference
BEDMAS, complete at last: Brackets → Exponents → Divide/Multiply (left to right) → Add/Subtract (left to right). Same order whether the numbers are whole, negative, decimal, or fraction.