# Mathematics for the RAE

### Powers of numbers

When, say, two of a certain number are multiplied together, that number is said to be 'raised to the power 2'. Thus 2 x 2 = 4 means that 2 raised to the power 2 is 4. In this case we would say 2 'squared' is 4 and write it as 22 = 4. The 'little 2 up in the air' is called an 'index'. Similarly, 2 x 2 x 2= 8 means that 2 raised to the power 3 is 8, or 2 'cubed' is 8, written as 23 = 8. Also 2 x 2 x 2 x 2 = 16. Here we have no alternative but to say 2 'to the power 4' = 16, or 24= 16.

The use of indices or the index notation is a very convenient way of expressing the large numbers which often occur in radio calculations, eg

100 = 10 x 10= 102

10,000 = 10 x 10 x 10 x 10 = 104

1,000,000 = 10 x 10 x 10 x 10 x 10 x 10 = 106

Note that 10 = 101 (the index here is taken for granted).

Similarly

Numbers expressed in the index notation are multiplied and divided by adding and subtracting respectively the indices.

We can do this as long as the 'base' is the same in each case. In the above examples, the 'base' is 10. For example, 102 x 22 = 100 x 4 = 400, which is neither 104 nor 24 !

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