Why does constant Kc in chemical equilibrium has no units?

Kc is the equilibrium constant and is the ratio of the activity of the reactants (numerator) to the activity of the product (denominator). The activity of each component is raised to the power of its corresponding chemical stoichiometric coefficient. Since the activity of each chemical is unitless, the equilibrium constant will also have no units.

Example:

For equilibrium of chemicals in the gas phase, each activity will be measured by its partial pressure (units of pressure) multiplied by its fugacity (units of 1/pressure), so the activity of each gas participating in the equilibrium will be unitless, and the corresponding ratio (Kc) will be unitless.