Let's say you wanted to find the cube root of 8
You write it on your paper like this: [tex]\sqrt[3]{8}[/tex]
In your calculator, you'd type this in: 8^(1/3)
The exponent of 1/3 corresponds to a cube root.
In general, the exponent of 1/n is for the nth root
The connection is [tex]\sqrt[n]{\text{x}} = \text{x}^{1/n}[/tex]