Numbers and operations · Ages 12–13

Powers worksheet

Part of: Working with numbers

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Numbers and operations · Ages 12–13

Numsprite
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Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

13.A computer virus infects 3 times as many computers each hour as the hour before. It infects 4 in hour 1. How many does it infect in hour 4?
Working:
Answer:
14.Tsz-ching tells a piece of news to 3 friends: that is round 1. After that, everyone who has just heard it tells 3 more people who haven't. How many people newly hear it in round 4?
Working:
Answer:
15.A cell splits once a day, 1 into 2. Starting with one, after 10 days there are 2^□ cells, that is ; a day later there are .
Fill in each blank
Working:
Answer:
16.A germ splits from 1 into 2 every 30 minutes. Starting with one germ, how many are there after 2 hours?
Working:
Answer:
17.Ming folds a sheet of paper in half 6 times, then opens it out. The creases split it into 2^□ parts, that is parts.
Fill in each blank
Working:
Answer:
18.A board has 1 grain of rice on square 1, 2 on square 2, 4 on square 3, each square double the one before. How many grains go on square 7?
Working:
Answer:

Show the answers and working

Powers worksheet: Answers and working

1. 64
4³ means 3 lots of 4 multiplied together, not 4 × 3 = 12. It is 64.
2. 4, 2
Count them: 4 appears 4 times and 8 twice, so it is 4⁴ × 8².
3. 81
3⁴ means 4 lots of 3 multiplied together, not 3 × 4 = 12. It is 81.
4. 5, 4
4 appears 5 times and 2 4 times: 4⁵ × 2⁴.
5. 300
10² is 1 followed by 2 zeros, so 3 × 10² = 300.
6. 5, 4
7 appears 5 times and 4 4 times: 7⁵ × 4⁴.
7. 31
Powers first: 2² = 4 and 3³ = 27; then add: 4 + 27 = 31.
8. 7
Divide 128 by 2 again and again: it takes 7 goes to reach 1, so 128 = 2⁷.
9. 7
Divide 2187 by 3 again and again: it takes 7 goes to reach 1, so 2187 = 3⁷.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 108 computers
Hour 4 is 3³ times hour 1: 4 × 3³ = 108.
14. 81 people
Each round is 3 times the one before: round 4 has 3⁴ = 81 people.
15. 10, 1024, 2048
Doubling each day: after 10 days, 2¹⁰ = 1024; a day later, double again: 2048.
16. 16 germs
2 hours hold 4 spells of 30 minutes, each doubling: 2⁴ = 16.
17. 6, 64
Each fold doubles the parts: 6 folds make 2⁶ = 64.
18. 64 grains
Square 1 has 2⁰ = 1 and square 2 has 2¹, so square 7 has 2⁶ = 64. Careful: not 2⁷.

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