  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!

1.
What is the result of 27 ÷ 28?
1/2
2
-1/2
-2
2(7 - 8) = 2-1 = 1/2 since the negative power is 1 over the positive power
2.
What index number must follow 3 to give 6,561?
7
8
9
10
6,561 = 81 x 81 = 34 x 34
3.
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
After 1 year 500 x 1.015; after 3 years 500 x 1.0153
4.
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
'30 days hath September, April, June and November .......' so the plant has been growing for 28 = 4 x 7 days; 20 x 27
5.
What is the result of dividing 25 by 625?
51
5-1
52
5-2
25 = 52; 625 = 54
6.
How many litres will fill a cube of side length 25 cm?
1.25
15.625
25.125
61.25
253 ÷ 1,000 = 56 ÷ 103. Remember 1,000 cm3 = 1 litre
7.
What is 0.24 as a power of 5?
5-1
5-2
5-4
5-5
0.2 = 1/5 = 5-1
8.
What is the result of 16 x 64 as a power of 2?
26
28
210
212
16 = 24; 64 = 26; 16 x 64 = 2(4 + 6)
9.
What is the result of 24 x 83?
1,992
8,192
65,536
99,664
Convert 83 to a power of 2 before adding the indices
10.
How many days are there in 29 x 33 x 54 seconds?
30
50
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 