Traditional option pricing models mostly assume that the market is frictionless, ignoring the impact of liquidity on option price. In response, this paper considers a digital power generalized exchange option pricing problem when the underlying asset has liquidity risk. We obtained a closed-form digital power option pricing formula in a incomplete market by measure transformation. Finally, numerical experiments were conducted by comparing the prices computed by the new formula with those from Monte-Carlo simulations, thereby validating the accuracy of the new formula. Building on this, the impact of liquidity on option prices was further investigated.