Numbers and operations · Ages 13–14
Multiplying and dividing powers worksheet
Part of: Laws of integral indices
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Multiplying and dividing powers worksheet
Numbers and operations · Ages 13–14
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.
Part A: Working out and filling in (2 marks each)
1.Fill in the index: 103 × 102 = 10□
Answer:
2.Fill in the index: 715 ÷ 73 = 7□
Answer:
3.Fill in the index: x11 × x6 = x□
Answer:
4.Simplify: 30x14 ÷ 5x3 = x□
Fill in each blank
Answer:
5.Simplify: 4x5 × 5x7 = x□
Fill in each blank
Answer:
6.Simplify: 5x4y4 × 6x7y7 = x□y□
Fill in each blank
Answer:
7.Fill in the index: 25 × 29 ÷ 26 = 2□
Answer:
8.Fill in the index: 105 × 105 ÷ 103 = 10□
Answer:
Part B: Choose, or true or false (2 marks each)
9.x3 × x5 = x8
True or false?
Answer:
10.x3 × x8 ÷ x5 = ?
- A. x16
- B. x19
- C. x11
- D. x6
Choose the right answer
Answer:
11.59 ÷ 53 = 53
True or false?
Answer:
12.38 ÷ 34 = 34
True or false?
Answer:
Part C: Word problems (4 marks each)
13.Tsz-ching says 29 is 24 times 25. Tsz-ching is right.
True or false?
Working:
Answer:
14.A computer does 211 operations a second. Running for 25 seconds, it does 2□ operations in all.
Working:
Answer:
15.Simplify 4x6 × 4x4 × x6. Put the steps in order.
- A. 16x6 × x4 × x6 = 16x10 × x6
- B. 16x10 × x6 = 16x16
- C. 4x6 × 4x4 × x6 = 16x6 × x4 × x6
Write the letters in the right order
Working:
Answer:
16.A store holds 109 grains of rice, shared equally into 105 bags. Each bag holds 10□ grains.
Working:
Answer:
17.A memory card holds 214 units, and each file takes 25 units. The card already has 27 files on it. How many more files can it take?
Working:
Answer:
18.A rectangle is 8x6 cm long and 9x6 cm wide. Its area is x□ cm².
Fill in each blank
Working:
Answer:
Show the answers and working
Multiplying and dividing powers worksheet: Answers and working
Part A: Working out and filling in
1. 5
The same base, so multiplying adds the indices: 3 + 2 = 5.
2. 12
The same base, so dividing subtracts the indices: 15 − 3 = 12.
3. 17
11 x's times 6 x's is 17 x's multiplied: 11 + 6 = 17.
4. 6, 11
Divide the numbers: 30 ÷ 5 = 6; subtract the indices: 14 − 3 = 11. So 6x11.
5. 20, 12
Multiply the numbers: 4 × 5 = 20; add the indices: 5 + 7 = 12. So 20x12.
6. 30, 11, 11
The numbers: 5 × 6 = 30; x's index 4 + 7 = 11; y's index 4 + 7 = 11. Each letter on its own.
7. 8
Add the indices multiplied and subtract the one divided: 5 + 9 − 6 = 8.
8. 7
Add the indices multiplied and subtract the one divided: 5 + 5 − 3 = 7.
Part B: Choose, or true or false
9. True
Multiplying adds the indices; it doesn't multiply them: x3 × x5 = x8.
10. D. x6
Left to right: the index is 3 + 8 − 5 = 6, so x6.
11. False
Dividing subtracts the indices; it doesn't divide them: 9 − 3 = 6.
12. True
Dividing subtracts the indices; it doesn't divide them: 8 − 4 = 4.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. True
29 ÷ 25 = 2^(9 − 5) = 24, so 24 times.
14. 16
In all = per second × seconds = 211 × 25 = 2^(11 + 5) = 216.
15. C → A → B
Multiply the numbers first, 4 × 4 = 16, then add x's indices one by one: 6 + 4 + 6 = 16.
16. 4
Each bag = 109 ÷ 105 = 10^(9 − 5) = 104.
17. 384 files
It takes 214 ÷ 25 = 29 = 512 files in all; 27 = 128 are there, so 512 − 128 = 384 more.
18. 72, 12
Area = length × width = 8x6 × 9x6: 8 × 9 = 72 and 6 + 6 = 12, so 72x12 cm².
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