So far we have looked at powers of ten that are whole number, either greater than one for numbers exceeding ten (eg 100 = 102), or less than one to represent one divided by the power of ten (eg 1 ÷ 1000 = 0.001 = 10-3). We can also use power notation to represent roots. For instance the square root of one hundred is written as:

 

√100 = 100½ or 1000.5

 

Using what you learnt about powers of powers in the previous section, you should be able to see that:

 

1000.5 = (102)0.5 = 10(2 x 0.5) = 101

 

The cube root raises the number to power one-third eg 10000.333 and the fifth root raises the number to power one-fifth eg 10000.2.

 

More generally, the 'xth' root of A is given by A(1/x).