In a large bowl, combine the first eight ingredients.
Gradually beat in oil.
Add eggs, one at a time, beating well after each.
Stir in the carrots, pineapple and pecans.
Transfer to a greased 8-inch round microwave-safe casserole dish.
Microwave, uncovered, at 70 percent power for 9-11 minutes, or until a moist area about 1 1/2 inches in diameter remains in the center (when touched, cake will cling to your finger while area underneath will be almost dry).