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Reading a manga at the moment and I encountered the following sentence:

オスといると、それこそネズミ算式に増えちゃいますから

If ねずみ算 means to 'multiply like rats' what is the significance of adding 式に増える?

I am also confused of what 式 actually means.

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This 式 on its own has a meaning of "manner" or "style". It is a common suffix used with a noun. ねずみ算 is just a noun, and 式 turns it to a no-adjective.

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