Preheat the oven to 180°C (350°F/Gas 4). Lightly grease and line a 30 × 20 cm (12 × 8 inch) cake tin. Place the eggs and sugar in a large bowl and, using an electric beater, beat until thick and pale. Add the carrot purée and oil and beat to combine. Sift over the flour and baking powder and mix thoroughly. Pour into the lined tin and bake for 1 hour or until an inserted skewer comes out clean. Remove from the tin and cool on a wire rack. Cut the cake into six 10 × 4 cm (4 × 1½ inch) portions. Set aside.