3^√27 = 27^1/3 

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As written this statement can be seen to be false since the right hand side becomes 3^1; the cube root of 27 is 3.  However, the left side is writen as 3^(SQR(27)) and the SQR(27) is not 1.  Therefore the statement is false.  It is also false if the radical index on the left was 3 not 2 .  That would make the left side 3^3 and that does not equal the right side.