Question

if x raised to power y = y raised to the power x then what is the value of x/y (x divided by y) raised to the power x upon y

Answer 1

${x}^{y} = y {}^{x} ---> \sqrt[y]{ {y}^{x} } = x \\ (\frac{x}{y} ) {}^{ \frac{x}{y} } = \frac{ {x}^{ \frac{x}{y} } }{ {y}^{ \frac{x}{y} } } = \sqrt[y]{ \frac{ {x}^{x} }{ {y}^{x} } } = \sqrt[y]{ \frac{ {x}^{x} }{ {x}^{y} } } \\ \sqrt[y]{ {x}^{x - y} } = {x}^{ \frac{x - y}{y} }$

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Answer 2

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