If x = 2 and y = 4, then (x/y)^x-y+(y/x)^y-x = ​

Question

If x = 2 and y = 4, then \((\frac{x}{y})^{x-y}+(\frac{y}{x})^{y-x}\) =

A. 4

B. 8

C. 12

D. 2

Answer 1

(2/4)^{2 – 4} + (4 / 2)^{4 – 2}

= (1/2)^-2 + 2²

= 2² + 2²

= 8