Lucy
Ask the AI Tutor
Need help with Level 7-8 Numbers - Indices? Ask our AI Tutor!
Lucy AI Tutor - Lucy
Connecting with Tutor...
Please wait while we establish connection
Lucy
Hi! I'm Lucy, your AI tutor. How can I help you with Level 7-8 Numbers - Indices today?
now
0/50 words
  1. Home
  2. KS3
  3. Maths
  4. Level 7-8 Numbers - Indices
Logo

Maths Quiz - Level 7-8 Numbers - Indices (Questions)

Indices show repeated multiplication. Learn square, cube and negative powers, apply index laws, and use powers of 10 to solve KS3 questions clearly and quickly.

Explore the Topic →
(quiz starts below)

Fascinating Fact:

Indices help describe money growth, since compound interest follows the formula A = P(1 + r)n, where n is the power of time.

In KS3 Maths, indices (powers) let us write repeated multiplication efficiently and calculate quickly. You’ll apply index laws, use powers of ten, and work confidently with standard form in real contexts.

Key Terms

  • Index (power): The small number that shows how many times a base is multiplied by itself, e.g., 34 = 3 × 3 × 3 × 3.
  • Base: The number being repeatedly multiplied, e.g., in 53 the base is 5.
  • Standard form: A way to write big or small numbers as a × 10n, where 1 ≤ a < 10 and n is an integer.

Frequently Asked Questions (Click to see answers)

What are the index laws in KS3?

Key rules: am × an = am+n, am ÷ an = am−n (a ≠ 0), and (am)n = amn.

How do zero and negative powers work?

For a ≠ 0, a0 = 1. A negative power gives a reciprocal: a−n = 1 / an; e.g., 2−3 = 1/8.

What does 10n mean in standard form?

It’s a power of ten used to scale numbers. For example, 3.2 × 104 = 32,000 and 5.6 × 10−3 = 0.0056.

Try These Related Quizzes

1. What is the result of 16 x 64 as a power of 2?
[ ] 26
[ ] 28
[ ] 210
[ ] 212
2. What is the result of 27 ÷ 28?
[ ] 1/2
[ ] 2
[ ] -1/2
[ ] -2
3. What is the result of dividing 25 by 625?
[ ] 51
[ ] 5-1
[ ] 52
[ ] 5-2
4. What is 0.24 as a power of 5?
[ ] 5-1
[ ] 5-2
[ ] 5-4
[ ] 5-5
5. What index number must follow 3 to give 6,561?
[ ] 7
[ ] 8
[ ] 9
[ ] 10
6. What is the result of 24 x 83?
[ ] 1,992
[ ] 8,192
[ ] 65,536
[ ] 99,664
7. How many litres will fill a cube of side length 25 cm?
[ ] 1.25
[ ] 15.625
[ ] 25.125
[ ] 61.25
8. How many days are there in 29 x 33 x 54 seconds?
[ ] 30
[ ] 50
[ ] 100
[ ] 125
9. A pond plant doubles its surface area every four days. If it covered an area of 20 cm2 on 17th June, what is its area on 15th July?
[ ] 2,560 cm2
[ ] 2.56 m2
[ ] 0.256 m2
[ ] 256 cm2
10. John started a savings account with a deposit of £500 at 1.5% compound interest per year. How much (to the nearest 1p) is the account worth after three years?
[ ] £168.75
[ ] £522.84
[ ] £760.44
[ ] £1,522.50

You can find more about this topic by visiting BBC Bitesize - Powers

© Education Quizzes. Please visit www.educationquizzes.com to subscribe
Logo
Maths Quiz - Level 7-8 Numbers - Indices (Answers)
1. What is the result of 16 x 64 as a power of 2?
[ ] 26
[ ] 28
[x] 210
[ ] 212
16 = 24; 64 = 26; 16 x 64 = 2(4 + 6)
2. What is the result of 27 ÷ 28?
[x] 1/2
[ ] 2
[ ] -1/2
[ ] -2
2(7 - 8) = 2-1 = 1/2 since the negative power is 1 over the positive power
3. What is the result of dividing 25 by 625?
[ ] 51
[ ] 5-1
[ ] 52
[x] 5-2
25 = 52; 625 = 54
4. What is 0.24 as a power of 5?
[ ] 5-1
[ ] 5-2
[x] 5-4
[ ] 5-5
0.2 = 1/5 = 5-1
5. What index number must follow 3 to give 6,561?
[ ] 7
[x] 8
[ ] 9
[ ] 10
6,561 = 81 x 81 = 34 x 34
6. What is the result of 24 x 83?
[ ] 1,992
[x] 8,192
[ ] 65,536
[ ] 99,664
Convert 83 to a power of 2 before adding the indices
7. How many litres will fill a cube of side length 25 cm?
[ ] 1.25
[x] 15.625
[ ] 25.125
[ ] 61.25
253 ÷ 1,000 = 56 ÷ 103. Remember 1,000 cm3 = 1 litre
8. How many days are there in 29 x 33 x 54 seconds?
[ ] 30
[ ] 50
[x] 100
[ ] 125
Divide by 60 x 60 = 24 x 32 x 52 to find the hours, then divide by 24 = 23 x 31 to find days
9. A pond plant doubles its surface area every four days. If it covered an area of 20 cm2 on 17th June, what is its area on 15th July?
[x] 2,560 cm2
[ ] 2.56 m2
[ ] 0.256 m2
[ ] 256 cm2
'30 days hath September, April, June and November .......' so the plant has been growing for 28 = 4 x 7 days; 20 x 27
10. John started a savings account with a deposit of £500 at 1.5% compound interest per year. How much (to the nearest 1p) is the account worth after three years?
[ ] £168.75
[x] £522.84
[ ] £760.44
[ ] £1,522.50
After 1 year 500 x 1.015; after 3 years 500 x 1.0153
© Education Quizzes. Please visit www.educationquizzes.com to subscribe