Can someone explain how

r = sqrt(1+(c-3)^2)

becomwa

r = (c^2-6c+10)^1/2

They expanded the inside of the square root.

An exponent of 1/2 corresponds to "square root"
An exponent of 1/3 corresponds to "cube root"
An exponent of 1/4 corresponds to "fourth root"

etc.