KS3 Maths Quiz
A pond plant doubles its surface area every four days.

# Level 7-8 Numbers - Indices

You'll come up against power numbers often in KS3 Maths. Power numbers, or indices, are the small numbers written above and to the right of other numbers. For example, cubed (3) and squared (2) are both types of indices.

In the Powers quiz you saw how, by writing numbers as powers of a common base, multiplication and division can be turned into addition or subtraction of indices. This makes calculations with large or small numbers much easier, as long as you follow the rules!

When multiplying add the powers, so 22 x 23 = 25. When dividing subtract the powers, so 25 ÷ 22 = 23. When working out a power of a number already raised to a power, multiply the powers, so the square of 24 = 28.

Let's find out whether you've got power over the powers! This quiz will give you plenty of practise. Good luck!

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1. 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?
After 1 year 500 x 1.015; after 3 years 500 x 1.0153
2. What is the result of 16 x 64 as a power of 2?
16 = 24; 64 = 26; 16 x 64 = 2(4 + 6)
3. How many days are there in 29 x 33 x 54 seconds?
Divide by 60 x 60 = 24 x 32 x 52 to find the hours, then divide by 24 = 23 x 31 to find days
4. How many litres will fill a cube of side length 25 cm?
253 ÷ 1,000 = 56 ÷ 103. Remember 1,000 cm3 = 1 litre
5. What is the result of 24 x 83?
Convert 83 to a power of 2 before adding the indices
6. What is the result of 27 ÷ 28?
2(7 - 8) = 2-1 = 1/2 since the negative power is 1 over the positive power
7. What is 0.24 as a power of 5?
0.2 = 1/5 = 5-1
8. What index number must follow 3 to give 6,561?
6,561 = 81 x 81 = 34 x 34
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?
'30 days hath September, April, June and November .......' so the plant has been growing for 28 = 4 x 7 days; 20 x 27
10. What is the result of dividing 25 by 625?
25 = 52; 625 = 54

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