Let T=T N Y W R, and let T=10 X+Y for an integer X and a digit Y. Suppose that a and b are real numbers satisfying a+\frac{1}{b}=Y and \frac{b}{a}=X. Compute (a b)^{4}+\frac{1}{(a b)^{4}}.
Let T=T N Y W R, and let T=10 X+Y for an integer X and a digit Y. Suppose that a and b are real numbers satisfying a+\frac{1}{b}=Y and \frac{b}{a}=X. Compute (a b)^{4}+\frac{1}{(a b)^{4}}.