Discussion

Explanation:

We need to given answer in terms of x, hence let us find value of y in terms of x.

Given, x^y = y^x
⇒ y = (x^y)^1/x = x^y/x 

Now, ${\left(\frac{\mathrm{x}}{\mathrm{y}}\right)}^{\frac{\mathrm{x}}{\mathrm{y}}}$ = ${\left(\frac{\mathrm{x}}{{\mathrm{x}}^{\mathrm{y}/\mathrm{x}}}\right)}^{\frac{\mathrm{x}}{\mathrm{y}}}$

= ${\left({\mathrm{x}}^{1-\mathrm{x}/\mathrm{y}}\right)}^{\frac{\mathrm{x}}{\mathrm{y}}}$

= ${\mathrm{x}}^{x/y-1}$

Hence, option (b).

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