If $x^{y} = y^{x}$ , then $(x / y)^{x / y}$ equals

x^{x / y}

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x^{(x / y) - 1}

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x^{y / x}

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x^{(y / x) - 1}

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Solution

The correct option is B $x^{(x / y) - 1}$
$x^{y} = y^{x}$
or $x = y^{x / y}$
or $y = y^{y / x}$
$∴ \frac{x}{y} = \frac{y^{x / y}}{y} = y^{(x / y) - 1} = (x^{x / y})^{[(x / y) - 1]}$
or ${(\frac{x}{y})}^{x / y} = {x^{x / y [(x / y) - 1]}}^{x / y} = x^{(x / y) - 1}$

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