# find for 12xy

#### debos

##### New member
if (81)^x=1/((125)^y) and x,y are integers then find the value of 12xy.

#### Subhotosh Khan

##### Super Moderator
Staff member
if (81)^x=1/((125)^y) and x,y are integers then find the value of 12xy.
Please follow the rules of submission at this forum - enunciated at:

Hint:

(81)^x=1/((125)^y)

(3)^(4x) = (5)^(-3y)

continue...

#### JeffM

##### Elite Member
This is the second time that you have been asked to read the submission guidelines. Please do so before starting any new threads.

I did not find Subhotosh's hint penetrated my frequently dim, and certainly insufficiently caffeinated, mind. So here is a different hint.

$$\displaystyle 81^x = \dfrac{1}{125^y} \implies 81^x * 125^y = 1.$$

Can x and y both be positive integers? Can they both be negative integers? Proceed

#### Subhotosh Khan

##### Super Moderator
Staff member
This is the second time that you have been asked to read the submission guidelines. Please do so before starting any new threads.

I did not find Subhotosh's hint penetrated my frequently dim, and certainly insufficiently caffeinated, mind. So here is a different hint.

$$\displaystyle 81^x = \dfrac{1}{125^y} \implies 81^x * 125^y = 1.$$

Can x and y both be positive integers? Can they both be negative integers? Proceed
I think you and I were going for the same conclusion. I am waiting for OP's response!

#### JeffM

##### Elite Member
I think you and I were going for the same conclusion. I am waiting for OP's response!
Subhotosh

We undoubtedly were, but the point of your hint was not obvious to me until I had pursued mine a while.

#### debos

##### New member
Please follow the rules of submission at this forum - enunciated at:

Hint:

(81)^x=1/((125)^y)

(3)^(4x) = (5)^(-3y)

continue...

#### Subhotosh Khan

##### Super Moderator
Staff member
Look at response #3 -

81x=125-y

81x∗125y = 1

Can x and y both be positive integers? Can they both be negative integers? Proceed

Last edited:

#### debos

##### New member
Look at response #3 -