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If I understand your description correctly, the diagram above should represent your question. Each "donut" is a pair of 12/36 gears joined to move simultaneously, while each donut drives the succeeding one with the ratios presented.
The text has been placed at the interface of each gear pair. The first circle drives the second one with a 1 to 3 reduction, while the center of the second gear drives the third. This is mechanically unsound, but suitable as a discussion diagram.
There are seven interfaces/reductions, which means your gear ratio is 1 to 3 raised to the 7th power. The final reduction is therefore 1 : 2187
If there is one more reduction, the ratio is 1 : 6561
If you did not have equal gears between each set, you would have to multiply the denominators of all the ratios together to calculate the final ratio.
From a mechanical standpoint, consider to create a planetary gear set. You can accomplish substantial reduction in a more compact design.