Question

if x^y=y^x then find (x/y) ^x/y

Answer 1

Given that
${x}^{y} = {y}^{x}$
So we can write that, y = x^(y/x)

And substituting the value to
$( { \frac{x}{y} )}^{ \frac{x}{y} }$
We get ,

{ X / X^(y/x) }^(x/y)

= {X^(x/y)}/X^1

= X^{(x/y)-1}

So the answer is option no. 2

That's it
Hope it helped ヾ(｡>﹏<｡)ﾉﾞ✧*。

Answer 2

Answer:

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

Step-by-step explanation:

Given : $x^y=y^x$

To Find: $(x/y) ^{x/y}$

Solution:

$x^y=y^x$

So,$x^{\frac{y}{x}}=y$

Now substitute this value of y in $(x/y) ^{x/y}$

$(\frac{x}{y})^{\frac{x}{y}}$

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

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

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

So, Option 2 is correct