SOLUTION: 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 whe

Question 825459: 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.
Please help.
Answer by unlockmath(1688) (Show Source): You can put this solution on YOUR website!
Hello,
Let's try it this way, it might make more sense. Set it up as a proportion:
81^x/1 = 1/(125^y)
Now cross multiply.
1=(81^x)(125^y)
From this we can see the only numbers that satisfy the equation is 0 for x and y.
Does that help?
RJ
www.math-unlock.com
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