Fractional indices are expressions in surds or irrational form. In other words, the expressions have index or indices in fraction form.
To understand fractional indices, consider the following examples:
62 = 36 Therefore = 6
23 = 8 Therefore = 2
Now consider = = 16
multiplied by itself gives 16, and multiplied by itself gives 16.
Hence and are the same.
Summarising the above, we can conclude that =
Example 2: Let’s now look at
= = 64
We can express the above expression also as = 64
So multiplied by itself thrice gives 64, and multiplied by itself thrice also gives 64.
So we can conclude that = meaning x power of one-third is equal to the cube root of x.
This leads to the generalisation that = meaning x power of one-n is equal to the nth root of x.
Learn about law of negative indices here