The first number is the magnification, the second number is the size of the objective (main) lens, in mm.
So a 10×40 magnifies things by a factor of 10 and the main lenses are 40mm across.
If you need more “power”, that usually means more magnification, but that would be a *narrower* field of view. If you want a wider field of view you need less magnification.
The size of the objective lenses is mostly about light gathering power (big lenses give you a brighter image, particularly in low light conditions), and also allow better detail.
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