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Powerful Numbers I am learning to solve multiplication problems with powers (exponents). e.g. 22 or 23 The square below is 4 cubes high and 4 cubes wide. The square below is 2 cubes high and 2 cubes wide. The square below is 3 cubes high and 3 cubes wide. We can work out how many cubes there are by working out 2 X 2 = 4 We can work out how many cubes there are by working out 3 X 3 = 9 Using exponents we can record this as 22 Using exponents we can Using exponents we can record this as 32 record this as 42 If I square root the 4. If I square root the 9. 4 I get 2. This is the length of the sides. 9 I get 3. This is the length of the sides. We can work out how many cubes there are by working out 4 X 4 = 16 If I square root the 16. 16 I 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 3X3=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 2X2= 4 23 2X2X2= 8 24 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 27 2) 22 4 3) 24 16 4) 34 81 5) 27 Click again when you have worked out all your answers. 128 Need some more practise? Try Pg47 & 48 of Teacher Tools Multiplication and Division Book Numeracy resources