---
title: "Order of operations with powers and roots"
description: "Use conventional notation for the priority of operations including brackets, powers, roots, and reciprocals; apply BIDMAS/BODMAS consistently to evaluate complex numerical expressions"
canonical: https://lightmysky.com/learn/mathematics/order-of-operations-with-powers-and-roots-mt_X5cypSGoGU
source: https://lightmysky.com/learn/mathematics/order-of-operations-with-powers-and-roots-mt_X5cypSGoGU.md
retrieved: 2026-10-19
---

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# 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

Subject: Mathematics · Area: Multiplication & Division · Ages 11 to 12
Page: https://lightmysky.com/learn/mathematics/order-of-operations-with-powers-and-roots-mt_X5cypSGoGU

## Ready when they can

- 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

## Lesson: Powers, roots, and the order of operations

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.

*(drawing: The power goes first: 2³ becomes 8. Then the division. Then the addition.)*

**Example.** 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.

**Tip.** 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.

**Recap.** Brackets first, then powers and roots, then multiply and divide, then add and subtract, and a number times its reciprocal always makes 1.

## Practice

20 questions on this page, each with its working shown.

## Needs first

- [Square and cube numbers](https://lightmysky.com/learn/mathematics/square-and-cube-numbers-mt_gxCIASSezX)
- [Integer powers and roots](https://lightmysky.com/learn/mathematics/integer-powers-and-roots-mt_hCVPYlF-7Y)
- [Order of operations](https://lightmysky.com/learn/mathematics/order-of-operations-mt_jHgRQ4hR0g)