Question

If $x^y=y^x$, what is the value of ${\left(\frac{x}{y}\right)}^{\frac{x}{y}}$?

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

Answer 1

Answer: (B)

$x^{\frac{x}{y}-1}$

$Now{x}^y=y^x\to y=x^{\frac{y}{x}}Nowwehave,{\left(\frac{x}{y}\right)}^{\frac{x}{y}}Substitutingthevalueofy,weget\to {\left(\frac{x}{x^{\frac{y}{x}}}\right)}^{\frac{x}{y}}={\left(x^{1-\frac{y}{x}}\right)}^{\frac{x}{y}}=x^{\frac{x}{y}-1}$