What does high melting point, high degree of hardness indicate about the strength of the bonding between ions/molecules? 

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A high melting point and hardness of a material indicates that the bonds between molecules that make up the material are quite strong.

A strong bond between molecules means that the bonds are much harder to break apart compared to weak bonds.

A hard material is hard because the bonds offer a lot of resistance when you try to deform the material, whereas the bonds between molecules in a soft material are easier to break apart offering less resistance to deformation.

The same can be said about melting a material.  Essentially, the stronger the bond the more resistance the bonds between molecules provide against deformation.

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