Preheat the oven to 350° F. In a medium sized bowl, using a hand mixer, blend the butter sugar until creamy. Gradually add the flour to the butter mixture at low speed until mixture is crumbly.
Transfer the flour mixture into the bottom of an 8 X 8 inch pan and press evenly across the bottom of the pan. Bake the crust for 15 minutes. Remove from the oven and cool on a wire rack.
TO MAKE THE LEMON FILLING
In a large mixing bowl, using a hand mixer at medium speed, mix the eggs until foamy. Add the sugar, lemon juice, flour, lemon zest, baking powder, and salt. Mix until well-blended.
Gently pour the lemon mixture over the partially baked crust. Return to the oven and bake for 20 minutes or until lemon filling has set. Cool on a wire rack. Sift powdered sugar evenly over top of cooled bars.