Question

Possible values of x and y satisfying (2x)5=(3y)6 are

Answer 1

Possible values of x and y satisfying (2x)5=(3y)6

(2x)5 = (3y)6

10x = 18y

x=(18/10) y

x= (9/5)y

Putting value of x= (9/5)y in (2x)5=(3y)6

2 X (9/5)y = 18y

(18/5)y = 18y

y = 5

Hence, the values are x= (9/5)y and y = 5

Answer 2

I think your question is ------> Possible values of x and y satisfying $\bf{(2x)^5=(3y)^6}$ are


solution :- $\bf{(2x)^5=(3y)^6}$
$\implies\bf{(2)^5x^5=3^6y^6}\\\implies\bf{32x^5=729y^6}$

here you can see that equation has two variable x and y so, it has so many solutions
let x = 1/2 , y = 1/3
Then, LHS = 32 (1/2)^5 = 32 × 1/32 = 1
RHS = 729y^6 = 729 × 1/729 = 1
LHS = RHS

hence, one solution is (1/2, 1/3)