Question 65

If $$x^{y} = y^{x}$$, then $$\left(\frac{x}{y}\right)^{\frac{x}{y}}$$

$$x^y=y^x$$
We shift the power y from LHS to RHS
==>Β $$x\ =\ y^{\frac{x}{y}}$$.
No we substitute the value ofΒ $$y^{\frac{x}{y}}$$Β inΒ $$\left(\ \frac{x}{y}\right)^{\frac{x}{y}}$$, we get:
$$\frac{x^{\frac{x}{y}}}{x}=x^{\frac{x}{y}-1}$$.

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