Evaluate without calculator or logarithm help

On my previous blog post(Evaluate $12^{\frac{1-(x+y)}{2(1-y)}}$), we're asked, without using the calculator and the help from logarithm, evaluate $\large12^\frac{1-(x+y)}{2(1-y)}$ provided $3=60^x$ and $5=60^y$.

Let do this problem as we're told, where we could not borrow help from calculator nor logarithms.

If we multiply the two given exponential equations, we get:

$3\cdot 5=60^x\cdot 60^y$
   
$3\cdot 5=60^{x+y}$

$3\cdot 5=5^{x+y}\cdot 12^{x+y}$

$3=5^{x+y-1}\cdot 12^{x+y}(*)$