Order of operations with powers and roots
Use conventional notation for the priority of operations including brackets, powers, roots, and reciprocals; apply BIDMAS/BODMAS consistently to evaluate complex numerical expressions
What a learner can do afterwards
- Evaluate expressions involving brackets, indices, and all four operations in the correct order
- Explain why the order of operations is necessary to avoid ambiguity
- Use the reciprocal of a number and understand that a number multiplied by its reciprocal gives 1
1 · Read
You already know to solve brackets first, then multiply and divide, then add and subtract. Now add two more steps: powers and roots. A power like 2³ means 2 × 2 × 2. A root like √9 asks what number times itself gives 9. Powers and roots come right after brackets, before you multiply, divide, add, or subtract.
Follow Maya as she solves (6 − 2)² ÷ 8 + 3. First the bracket: 6 − 2 = 4. Next the power: 4² = 16. Then division: 16 ÷ 8 = 2. Last, addition: 2 + 3 = 5. The answer is 5.
Order of operations exists so everyone gets the same answer. Without it, 2 + 3 × 4 could mean 5 × 4 = 20, or 2 + 12 = 14, depending on the order you pick. Mathematicians agreed on one order, so the answer is always 14.
A reciprocal is what you multiply a number by to get 1. The reciprocal of 5 is 1/5, because 5 × 1/5 = 1. To find the reciprocal of a whole number, flip it into a fraction with 1 on top.
Brackets first, then powers and roots, then multiply and divide, then add and subtract, and a number times its reciprocal always makes 1.
2 · Watch
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20 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.