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Year 8 · Standard form
Understand positive and negative powers of 10
Definition
An index (or power) tells you how many times to multiply a number by itself. 2³ means 2 × 2 × 2 = 8. The small raised number is the index; the big number is the base.
Why Do I Have to Learn This?
Indices are a short way to write repeated multiplying, like 2 to the power 5. They power everything from computer memory to population growth.
Key Rules:
- 1. To multiply powers of the same base, add the indices: x² × x³ = x⁵.
- 2. To divide, subtract the indices.
- 3. A square root undoes squaring; a cube root undoes cubing.
Remember:
- •2³ is 2 × 2 × 2 = 8, not 2 × 3 = 6.
- •Anything (except 0) to the power 0 is 1.
- •The index rules only work when the base is the same.
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 Understand positive and negative powers of 10 Worksheet
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Next: Standard form (Year 9)
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