Powerful Numbers

I am learning to solve multiplication problems with powers (exponents).

e.g. 22 or 23

The square below is 2 cubes high and 2 cubes wide.

We can work out how many cubes there are by working out 2 X 2 = 4

Using exponents we can record this as 22

If I square root the 4.

4I get 2. This is the length of the sides.

The square below is 3 cubes high and 3 cubes wide.

We can work out how many cubes there are by working out 3 X 3 = 9

Using exponents we can record this as 32

If I square root the 9.

9I get 3. This is the length of the sides.

The square below is 4 cubes high and 4 cubes wide.

We can work out how many cubes there are by working out 4 X 4 = 16

Using exponents we can record this as 42

If I square root the 16.

16I get 2. This is the length of the sides.

33 Can be represented by a cube that is 3 small cubes high, wide and deep.

We can work out how many small cubes were used to make these by calculating 33

33 = 3 X 3 X 3

3 X 3 = 9 9 X 3 = 27

43 Can be represented by a cube that is 4 small cubes high, wide and deep.

We can work out how many small cubes were used to make these by calculating 43

43 = 4 X 4 X 4

4 X 4 = 16 16 X 4 = 64

Numbers can be raised to powers of 4, 5, 6 etc.

These numbers get big very quickly. Lets look at a couple of examples. Try to work these out as we go.

22

23

24

2 X 2 = 4

2 X 2 X 2 = 8

2 X 2 X 2 X 2 = 16

25 2 X 2 X 2 X 2 X 2 = 32

26 2 X 2 X 2 X 2 X 2 X 2 = 64

Work out answers to the questions below.

1) 33

2) 22

3) 24

4) 34

5) 27

Need some more practise? Try Pg47 & 48 of Teacher Tools Multiplication and Division Book Numeracy resources

Click again when you have worked out all your answers.

27

4

16

81

128