Question about EAY different, question, holding, instead, annual

Roflnadal

This has been bothering me for a little while:
I have a 90 day holding period yield of 1.3%.  The annual rate would be:
(1 + 0.013)^(365/90) -1 = 0.0537787
The BDY would be:
2 * [(1 + 0.013)^(365/180) -1] = 0.0530745
along the same lines, if I take the annual rate and try to get back to the BDY:
2 * [(1 +  0.0537787)^(.5) -1] = 0.0530745
HOWEVER, my question is why do I have to use 0.5 as the exponent to get back to the semi-annual rate instead of 180/365?  If I use 180/365 I get a different number:
2 * [(1 +  0.0537787)^(180/365) -1] = 0.0523380