Exponents: squares and cubes
What 3⁴ means, square and cube numbers as pictures, and powers of 10. Read one step, play with it, then tap “I understand this”.
Base and exponent
In 34 3 is the base and 4 is the exponent. It means 3 × 3 × 3 × 3 = 81, not 3 × 4!
The power machine
Change the base and exponent.
The biggest mistake: 52 = 10. No! 52 = 5 × 5 = 25.
It is a shortcut, just like multiplying is a shortcut for adding. Ten 2s multiplied together you write short as 2¹⁰.
Squares and cubes
A number squared (²) makes a square; a number cubed (³) makes a cube.
Build it
Choose square or cube and change the side.
Know the squares up to 12² = 144 and the cubes up to 5³ = 125 by heart.
A square of 5 by 5 blocks has 5 × 5 = 25 blocks, so 5² is called “five squared”. A cube of 3 by 3 by 3 has 3 × 3 × 3 = 27 blocks: “three cubed”.
Powers of 10
| 101 | 10 |
| 102 | 100 |
| 103 | 1 000 |
| 106 | 1 000 000 |
The exponent of 10 tells you how many zeros come after the 1.
In a sum with powers, do the powers after brackets but before multiply and divide: 2 + 32 × 2 = 2 + 9 × 2 = 20.
Check yourself
- 3⁴ = 3 × 3 × 3 × 3 = 81, not 3 × 4.
- Squared: a number times itself (5² = 25). Cubed: three times (2³ = 8).
- 10ⁿ is a 1 with n zeros.
Write these points in your maths book. Read them again the night before the test.
Quick questions
Tap an answer. If you get one wrong, read why and go back to that step. You get new questions every time.
You ticked all 3 steps! Now you are ready for the quiz.- Practice sheet for this classQuestions + memo · 2 A4 pagesPractice sheet
- Numbers16 pages · PDFPaperMemo
Ready for more? The Grade 6 exponents quiz gives you new questions every time.
- One step a day is enough. Ten calm minutes work better than an hour the night before the test.
- A car question: “What is 9 squared? And the square root of 81?” Children like going back and forth.
- Ask your child to tell you the rule in their own words. If they can explain it, they understand it.
- The ticks (“I understand this”) are saved on this device only. We never ask for names or emails.
Follows CAPS for Grade 6 Maths. Always check your teacher’s notes and textbook too.