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 2^{2} x 2^{3} = 2^{5}. When dividing subtract the powers, so 2^{5} ÷ 2^{2} = 2^{3}. When working out a power of a number already raised to a power, multiply the powers, so the square of 2^{4} = 2^{8}.

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 0.2^{4} as a power of 5?

5^{-1}

5^{-2}

5^{-4}

5^{-5}

2.

A pond plant doubles its surface area every four days. If it covered an area of 20 cm^{2} on 17^{th} June, what is its area on 15^{th} July?

2,560 cm^{2}

2.56 m^{2}

0.256 m^{2}

256 cm^{2}

'30 days hath September, April, June and November .......' so the plant has been growing for 28 = 4 x 7 days; 20 x 2^{7}

3.

What is the result of 2^{7} ÷ 2^{8}?

1/2

2

-1/2

-2

2^{(7 - 8)} = 2^{-1} = 1/2 since the negative power is 1 over the positive power

4.

What index number must follow 3 to give 6,561?

7

8

9

10

6,561 = 81 x 81 = 3^{4} x 3^{4}

5.

What is the result of 2^{4} x 8^{3}?

1,992

8,192

65,536

99,664

Convert 8^{3} to a power of 2 before adding the indices

6.

What is the result of 16 x 64 as a power of 2?

2^{6}

2^{8}

2^{10}

2^{12}

16 = 2^{4}; 64 = 2^{6}; 16 x 64 = 2^{(4 + 6)}

7.

How many days are there in 2^{9} x 3^{3} x 5^{4} seconds?

30

50

100

125

Divide by 60 x 60 = 2^{4} x 3^{2} x 5^{2} to find the hours, then divide by 24 = 2^{3} x 3^{1} to find days

8.

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 1.015^{3}

9.

How many litres will fill a cube of side length 25 cm?

1.25

15.625

25.125

61.25

25^{3} ÷ 1,000 = 5^{6} ÷ 10^{3}. Remember 1,000 cm^{3} = 1 litre

10.

What is the result of dividing 25 by 625?

5^{1}

5^{-1}

5^{2}

5^{-2}

25 = 5^{2}; 625 = 5^{4}

^{-1}