Powers, Indices, LCM and GCF
Primary 6 · Mathematics
Powers, Indices, LCM and GCF
Lesson 1 of 6
25 min
Let's begin
Mugisha folds a sheet of paper in half. Now it has 2 layers. He folds it again: 4 layers. Again: 8 layers. After 5 folds, the number of layers is 2 × 2 × 2 × 2 × 2. Writing all those 2s is slow. Mathematicians have a short way to write it.
2 × 2 × 2 × 2 × 2 = 2⁵
So after 5 folds Mugisha has 2⁵ = 2 × 2 × 2 × 2 × 2 = 32 layers.
5³ does not mean 5 × 3. It means 5 × 5 × 5 = 125. And 4³ does not mean 4 + 4 + 4; it means 4 × 4 × 4 = 64.
Worked example 1
3⁴ = 3 × 3 × 3 × 3. Multiply step by step: 3 × 3 = 9, 9 × 3 = 27, 27 × 3 = 81.
Worked example 2
2³ × 5² = (2 × 2 × 2) × (5 × 5) = 8 × 25 = 200.
Any number to the power 1 is just itself: 9¹ = 9.
| Power | Meaning | Value |
|---|---|---|
| 10¹ | 10 | 10 |
| 10² | 10 × 10 | 100 |
| 10³ | 10 × 10 × 10 | 1 000 |
| 10⁶ | 10 × 10 × 10 × 10 × 10 × 10 | 1 000 000 |
The index tells you how many zeros follow the 1. Powers of 10 help us write numbers in expanded form: 3 405 = 3 × 10³ + 4 × 10² + 5.
Tip
Count the copies. The index counts how many copies of the base you multiply together. 2⁵ is five 2s multiplied, never 2 × 5.
Work each one in your exercise book first, then tap Show answer to check.
Write 7 × 7 × 7 × 7 as a power. Name the base and the index.
Answer: 7⁴. The base is 7 and the index is 4.
Work out 2⁶.
Answer: 2 × 2 × 2 × 2 × 2 × 2 = 64.
Work out 4² × 10².
Answer: 16 × 100 = 1600.
Write 1 000 000 as a power of 10.
Answer: 10⁶, because there are six zeros.
Which is bigger, 2⁴ or 4²?
Answer: They are equal: 2⁴ = 16 and 4² = 16.
What you learned today
Sources and credits
The stories, Rwandan worked examples and practice questions were written by Ganzaa.
Quick check
What does 6³ mean?
