Question

If x^y=y^x,then (x/y)^x/y is equal to​

Answer 1

Answer:

may be it's answer is

(y/x)^y/x

Answer 2

Answer:

(x/y)^(x/y) = y^((x/y) - 1)(x/y)

OR

(x/y)^(x/y) = x^((x/y) - 1)

Step-by-step explanation:

We must know certain important results in order for us to solve this problem,

If a^m = n

then,

a = 'm'√n ('m' shows root of mth power)

For ex:- 2³ = 8

2 = ³√8

Also,

'm'√a = a^(1/m)

and,

(a^m)/(a^n) = a^(m - n)

We are given,

x^y = y^x

Thus,

x^y = y^x

x = 'y'√(y^x)

x = y^(x/y) ------ 1

OR

y = x^(y/x) ------ 2

Now, we must find (x/y)^(x/y)

From eq.1 we get,

(x/y)^(x/y) = (y^(x/y)/y¹)^(x/y)

(x/y)^(x/y) = y^((x/y) - 1)^(x/y)

(x/y)^(x/y) = y^((x/y) - 1)(x/y)

OR

From eq.2 we get,

(x/y)^(x/y) = (x/(x^(y/x)))^(x/y)

(x/y)^(x/y) = (x^(x/y))/(x^(y/x)(x/y))

(x/y)^(x/y) = (x^(x/y))/x¹

(x/y)^(x/y) = x^((x/y) - 1)

It might be a bit difficult to understand so I have also uploaded an image of my written work

Hope it helped and you understood it........All the best