If \( \Large X^{y}=Y^{z},\ then\ \left(\frac{X}{Y}\right)^{x/y} \) equals

A) \( \Large X^{x/y} \)
B) \( \Large X^{ \left(x/y\right)-1 } \)

C) \( \Large X^{y/x} \)

Correct answer:
B) \( \Large X^{ \left(x/y\right)-1 } \)

Description for Correct answer:
\( \Large X^{y}=Y^{x} \)

\( \Large X = \left(Y\right)^{\frac{x}{y}} \)

\( \Large X.X^{-\frac{x}{y}} = Y^{x/y}.X^{-x/y} \)

\( \Large X^{1-x/y} = \left(\frac{Y}{X}\right)^{x/y} \)

\( \Large \left(\frac{X}{Y}\right)^{x/y} = X^{ \left(x/y\right)-1 } \)

Please provide the error details in above question

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