I've rewritten the reactions here for clarity.I left out all of the matter phase subscripts because they aren't particularly relevant for classifying the reactions.
`Cu(OH)_2 -> CuO + H_2O`
`CuO + 2H^+ + 5H_2O -> Cu(H_2O)_6^(2+)`
` Cu(H_2O)_6^(2+) + Zn -> Cu + Zn^(2+) + 6H_2O`
Reaction 1, where copper (II) hydroxide produces copper (II) oxide and water, can be characterized as a decomposition reaction or as dehydration, because you're basically just pulling a water molecule out of the copper hydroxide. Decomposition reactions can be recognized by the fact that they always have more product molecules than reactant molecules.
Reaction 2, in which copper (II) oxide, two hydrogen cations and five water molecules produce the hexaquacopper (II) ion, could technically be seen as two separate reactions. Hexaquacopper (II) is simply the copper +2 cation dissolved in water; the ion has six water molecules associated with it due to its charge. Neutral copper and oxide compounds don't dissolve in water, so, looking back at the reaction, the copper (II) oxide needed to become charged in order for it to dissolve.
Therefore, this reaction can be seen as two synthesis reactions combined into a single statement. Synthesis reactions are the opposite of decomposition, so they can usually be recognized by the fact that they have fewer product molecules than reactants.
Reaction 3 is another combination:
- The zinc changes its oxidation state from 0 to +2, so there is definitely a transfer of electrons taking place; therefore this must be some kind of redox.
- After the redox occurs, the copper has lost its charge, and therefore returned to an insoluble state. The water atoms dissociate from the copper, which can be seen as another decomposition/dehydration.