Question

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

• A. 0
• B. 1
• C. $x^{\frac{x}{y}-1}$
• D. $x^{\frac{x}{y}}$

Answer 1

The correct option is C $x^{\frac{x}{y}-1}$

$x^y=y^x$

$\Rightarrow y=x^{\frac{y}{x}}$

$\therefore {\left(\frac{x}{y}\right)}^{\frac{x}{y}}={\left(\frac{x}{x^{\frac{y}{x}}}\right)}^{\frac{x}{y}}$

$\Rightarrow x^{(\frac{x}{y}-1)}$