How to prove that sodium hydroxide is a base with the help of an equation for the reaction

The easy way is to place a drop of phenolphthalein in it. It will turn pink. The equation isn't easy to write. Another way, with an equation easier to write is to treat the NaOH with NH4Cl.

NH4Cl + NaOH ==> NH3 + NaCl + H2O
The odor of NH3 is not easily mistaken.