Why do thick lenses have more power than the thinner ones?

Solution:

A thick lens has greater curvature or lesser focal length, whereas a thin  lens has lesser curvature or greater focal length. 

We know that the power of the lens is inversely proportional to the focal length of the lens. Hence, the lens with a shorter focal length will have more power or higher refraction (causes more bending of light rays). While the lens with a longer focal length will have less power or low refraction (causes less bending of light rays).

Thus, a thick  lens has more power, as it has a lesser focal length.

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