Let P = 2^{1/2} \cdot 4^{1/4} \cdot 8^{1/8} \cdot 16^{1/16} Then P can be expressed in the form \sqrt[a]{b}, where a and b are positive integers. Find the smallest possible value of a+b.
P = 2^(1/2) * 4^(1/4) * 8^(1/8)* 16^(1/16)
P = 2^(1/2) * (2^2)^(1/4) * (2^3)^(1/8) * (2^4)^(1/16)
P = 2^(1/2)* 2^(1/2) *2^(3/8) * 2^(1/4)
P = 2^[ ( 4 + 4 + 3 + 2) / 8 ]
P = 2^( 13 / 8)
P = 8 √ (2^13)
a + b = 8 + 2^13 = 8 + 8192 = 8200
+1088 
