The expression \(x[n]y\) is defined for positive values of \(x\) and \(y\) and for positive integer values of \(n\) as

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The expression \(x[n]y\) is defined for positive values of \(x\) and \(y\) and for positive integer values of \(n\) as follows:

\(x[1]y = x^y,\)
If \(n\) is odd, \(x[n+1]y = (x[n]y)^x,\)
If \(n\) is even, \(x[n+1]y = (x[n]y)^y.\)

If \(y = \dfrac12\) and \(x[4]y = 2,\) then \(x =\)

A. \(\dfrac14\)

B. \(\dfrac12\)

C. \(1\)

D. \(2\)

E. \(4\)

Answer: D

Source: Manhattan GMAT