what does the prime factor decomposition of a perfect square look like
all terms are to an even power:
eg: 36 = 22 * 32
2025 (452) = 34 * 52
negative indices
fractional indices
1/x/y
y/x
i.e. root12/root6 = root2
just divide component parts:
14/16 = 7/8
root30/root3 = root10