Working with numbers · Ages 12–13
Powers
an is n lots of a multiplied, not a × n.
How to do it
Method
a^n is n lots of a multiplied, not a × n
25 = 2 × 2 × 2 × 2 × 2 = 32
Another way
Double again and again
2 → 4 → 8 → 16 → 32
In full
an (a to the power n) means n lots of a multiplied: a is the base, n the index. 25 = 2 × 2 × 2 × 2 × 2 = 32, not 2 × 5 = 10. Work it out one step at a time: 2, 4, 8, 16, 32. The same number multiplied again and again can be written as a power: 3 × 3 × 3 × 3 = 34. In a mixed calculation, powers come before multiplying and dividing.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
7 × 2 × 7 × 7 × 2 × 7 = 7□ × 2□
Fill in each blank
Show the answer and working
Answer: 4, 2
Count them: 7 appears 4 times and 2 twice, so it is 74 × 22.
Example 2
2 × 104 =
Show the answer and working
Answer: 20000
104 is 1 followed by 4 zeros, so 2 × 104 = 20000.
Example 3
63 = 216
True or false?
Show the answer and working
Answer: True
63 is 3 lots of 6 multiplied: 216. It is 6 × 3 that makes 18.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.43 =
Answer:
2.3 × 5 × 3 × 3 × 5 × 3 = 3□ × 5□
Fill in each blank
Answer:
3.4 × 5 × 4 × 5 × 5 × 4 × 4 × 5 × 5 = 5□ × 4□
Fill in each blank
Answer:
4.44 = 16
True or false?
Answer:
5.42 + 33 =
Answer:
All the answers
- 1. 64
- 2. 4, 2
- 3. 5, 4
- 4. False
- 5. 43
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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