Numbers and operations · Ages 13–14
Writing powers with the same base worksheet
Part of: Laws of integral indices
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Writing powers with the same base 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: 181 = 3□
Answer:
2.Fill in the index: 49 = 7□
Answer:
3.As a power of 3: 813 = 3□
Answer:
4.As a power of 2: 42 × 162 = 2□
Answer:
5.272 × 94 = (3□)2 × (3□)4 = 3□
Fill in each blank
Answer:
6.Solve: 81x = 3, x =
Answer in simplest form
Answer:
7.As a power of 3: 812 ÷ 276 = 3□
Answer:
8.Solve: 5^(x + 5) = 125, x =
Answer:
9.As a power of 3: 36 ÷ 816 = 3□
Answer:
Part B: Choose, or true or false (2 marks each)
10.93 × 273 = ?
- A. 2436
- B. 315
- C. 96
- D. 36
Choose the right answer
Answer:
11.95 × 272 = ?
- A. 316
- B. 37
- C. 2437
- D. 97
Choose the right answer
Answer:
12.42 × 83 = 213
True or false?
Answer:
Part C: Word problems (4 marks each)
13.Write 813 × 275 as a power of 3. Put the steps in order.
- A. 813 × 275 = (34)3 × (33)5
- B. 312 × 315 = 327
- C. (34)3 × (33)5 = 312 × 315
Write the letters in the right order
Working:
Answer:
14.Someone writes 814 × 93 as a power of 3 and gets 37. What is wrong? What is the right index?
- (1)81 and 9 can both be written as powers of 3
- (2)814 × 93 = 34 × 33
- (3)= 37
Find the wrong step, then write the right answer
Working:
Answer:
15.Ming says 96 = 275. Ming is right.
True or false?
Working:
Answer:
16.Which of these equals 166?
- A. 224
- B. 1624
- C. 26
- D. 210
Choose the right answer
Working:
Answer:
17.Solve 2^(x + 1) = 4x. What is x?
Answer in simplest form
Working:
Answer:
18.A storage device has 82 bytes. As a power of 2, it is 2□ bytes.
Working:
Answer:
Show the answers and working
Writing powers with the same base worksheet: Answers and working
Part A: Working out and filling in
1. −4
81 = 34; the reciprocal changes the index's sign: 181 = 3−4. So −4.
2. 2
Keep multiplying by 7 and count how many 7's make 49: 2.
3. 12
81 = 34, so 813 = (34)3 = 312.
4. 12
42 = 2^(2 × 2) and 162 = 2^(4 × 2); multiplying adds the indices: 12.
5. 3, 2, 14
27 = 33 and 9 = 32; the index: 3 × 2 + 2 × 4 = 14.
6. 14
Both sides as powers of 3: 3^(4x) = 31, so 4x = 1 and x = 14.
7. −10
3^(4 × 2) ÷ 3^(3 × 6): subtract the indices, −10.
8. −2
125 = 53; with the same base the indices are equal: x + 5 = 3, x = −2.
9. −18
3^(1 × 6) ÷ 3^(4 × 6): subtract the indices, −18.
Part B: Choose, or true or false
10. B. 315
93 × 273 = 3^(2 × 3) × 3^(3 × 3) = 315.
11. A. 316
95 × 272 = 3^(2 × 5) × 3^(3 × 2) = 316.
12. True
One base first: 42 × 83 = 2^(2 × 2 + 3 × 3) = 213; the bases can't be multiplied with the indices added.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. A → C → B
Change the bases, then a power of a power (multiply the indices), then multiply one base (add them): 12 + 15 = 27.
14. 22
81 = 34 and 9 = 32, not 3: 814 × 93 = 3^(4 × 4) × 3^(2 × 3) = 322.
15. False
Both as powers of 3: 96 = 3^(2 × 6) and 275 = 3^(3 × 5); they are equal only when the indices are.
16. A. 224
166 = (24)6 = 2^(4 × 6) = 224.
17. 1
Both as powers of 2: 2^(1(x + 1)) = 2^(2x), so x + 1 = 2x and x = 1.
18. 6
8 = 23, so 82 = (23)2 = 26.
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