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There is, indeed, an easy way. All these numbers can be expressed as powers of 2.

236 = 236

4 = 22 so 417 = (22)17 = 22*17 = 234

16 = 24 so 1610 = (24)10 = 24*10 = 240

32 = 25 so 327 = (25)7 = 25*7 = 235

64 = 26 so 645 = (26)5 = 26*5 = 230

The task of ordering them I leave to you.

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