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Year 9
Powers & Indices
Definition
A power tells you how many times to multiply a number by itself, written with a small raised index. A root is the inverse: a square root undoes squaring.
Why Do I Have to Learn This?
Powers pack repeated multiplication into a short form and roots undo them, which is how you handle areas, volumes and very large or very small numbers.
Key Rules:
- 1. The index shows how many times the base is multiplied.
- 2. Squaring and square rooting are inverse operations.
- 3. A cube root undoes cubing.
Remember:
- •3² means 3 × 3 = 9, not 3 × 2.
- •√49 = 7 because 7² = 49.
- •Any power of 1 is 1.
Don’t Forget...
- •Don’t read 3² as 3 × 2; it means 3 × 3.
- •Don’t forget a square root undoes a square: √49 is 7 because 7² is 49.
- •Don’t try to find a whole-number root of a number that is not a perfect square.
Cube
A solid with six square faces, all the same size. Volume = side × side × side, written side³.
A dice and a sugar cube are cubes.
Animated Example:
2
×2
×2
23 = 2 × 2 × 2 = 8
Free Powers & Indices Worksheet
Download free worksheets and practise today.
Every download has a fresh set of questions.
Let’s Practise the Concept
Step 1 of 3
Put them in order
Tap the numbers from smallest to largest.
In order so far: nothing yet