1.4 Roots and fractional indices
To see what fractional indices mean in practice a good place to start is with this example:
Using Rule 3 and 1 this can be written as follows:
This shows that 21/2 is a way to represent the square root of 2. Since .
Extending this a1/3 is the cube root of a and can be written as . a1/4 is the fourth root of a, written as .
So it follows that:
a1/n is the nth root of a and can be written as .
If you use Rule 3 to write ap/q as , you should now be able to see that ap/q is the qth root of ap which is written as .
Rules 1, 2, and 3 all work with fractional indices.
Before moving on to another topic, you’ll learn what the power of zero means.