Sodium hydroxide

NaOH, is an ionic compound and all ionic compounds are solids because the opposite charges of the cations and anions "glue" the particles together.

Important chemical fact:
When sodium hydroxide dissolves in water, a LOT of HEAT energy is released.

10 g of NaOH dissolved in 100 mL of water could raise the temperature of the water to boiling. If not evenly mixed some water would be superheated and splatter this concentrated lye solution over the person mixing it.

When dissolving sodium hydroxide add the NaOH slowly to cold water.
Adding water directly to sodium hydroxide solid is dangerous because you have a small volume of water that will absorb a large amount of heat.

Most hydroxides are insoluble, but the rule that all alkali metal compounds are soluble trumps the hydroxide insoluble rule. The polar charges of water can neutralize the inter-ionic forces and dissolve the sodium hydroxide

NaOH(aq) is misleading. The solution only contains Na⁺(aq) and OH^-(aq) since sodium hydroxide 100% ionizes. 
There is no NaOH(aq), there is only Na⁺(aq) and OH^-(aq).

Soluble ionic compounds completely dissociate.

Copper (II) nitrate

This picture is of the common form of copper(II) nitrate. As with many ionic compounds, it is a hydrate and the correct formula would be Cu(NO₃)₂•3H₂O(s). So the correct name would really be copper(II) nitrate trihydrate. Anhydrous copper(II) nitrate is white.

The copper ions attract water around them in a fixed ratio with a strong enough bond that the substance is a solid. The water molecules in the hydrate surrounding the copper(II) ion form a complex that produces the brilliant blue color.

This compound is often referred to by its older name cupric nitrate. (Cupric is the old name for copper (II) and cuprous is the old name for copper(I).

Cu(NO₃)₂ is soluble.
All nitrates are soluble. This is an important rule that you must memorize. Nitrates, just like alkali metals never form precipitates

Cu(NO₃)₂(aq) is misleading since copper(II) nitrate 100% ionizes. 
There is no Cu(NO₃)₂, there is only Cu²⁺(aq) and NO₃^-(aq) ions.

When the two solutions are mixed all four ions can interact.

Na⁺(aq) + OH^-(aq) + Cu²⁺(aq) + NO₃^-(aq)

There is a chance for the copper ions to attract to the hydroxide ions and the nitrate ions attract to the sodium ions. The new combinations of cations and anions are

Na⁺(aq) and NO₃^-(aq)

Cu²⁺(aq) and OH^-(aq)

The Na⁺(aq) and NO₃^-(aq) ions will not combine in aqueous solution since they are soluble.
However the Cu²⁺(aq) and OH^-(aq) attract one another so much that they will combine to make a solid, a precipitate. Most hydroxides are insoluble.

Thus the precipitate Cu(OH)₂ (s) forms. T
T he net ionic reaction is:

Cu²⁺(aq) + 2OH^-(aq) → Cu(OH)₂ (s)

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