Question

If \(x^y = y^x\) then \(\left(\frac{x}{y}\right)^{x/y}\) is

• A. \(x(y/y)\)
• B. \(\left(\frac{x}{y}\right)^{y/x}\)
• C. \(x^{(x+1)}\)
• D. \(y^y\)

Hint:

Always simplify expressions carefully when given relationships between exponents.

Answer 1

The Correct Option is B

From the given equation \(x^y = y^x\), we find that the simplified expression for \(\left(\frac{x}{y}\right)^{x/y}\) simplifies to \(\left(\frac{x}{y}\right)^{y/x}\). Thus, the correct answer is \(\left(\frac{x}{y}\right)^{y/x}\).