# 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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