I am solving a 7th grade text book and came across this question.
$81^x = 1/(125^y)$ where $x$ and $y$ are integers. Find $12xy$.
The answer given is $0$. While I can understand that when $x$ & $y$ are $0$ the above equation is satisfied, I can't seem to figure how to arrive at the conclusion.
I tried something like:
--> (3^4x)(5^3y) = 1
--> 3^(4x + 3ky) = 1 where k is such that 3^k = 5
--> 4x + 3ky = 0
But with the above am not able to establish that $12xy$ is $0$.
Thank you, Ramana