First things first, preheat your oven to 350°F (175°C),
grease with butter and flour a rectangular 9x13 nonstick cake pan.
In your blender, throw in those chopped carrots, eggs, and vegetable oil. Blend until you've got a smooth, orange mix.
In a large bowl, sift together the flour, sugar, and baking powder. Gently pour in the carrot mixture and mix until smooth. No need to overmix the batter as it will result in a stiff cake. (Remember to use a rubber spatula to scrape everything off your blender and into your large bowl. )
Pour batter into the prepared pan. Bake it, in your preheated oven, for roughly 40-50 minutes or until a toothpick comes out clean.
Once the cake's done, let it cool down on a wire rack.