Preheat the oven to 350°F.
In a large bowl, mix flour, baking soda, baking powder, and salt. Set aside.
In the bowl of an electric mixer, add eggs and sugar. Whip the eggs and sugar on high until they turn light and fluffy, about 2 minutes. Slowly add in the olive oil and whip for another 2 minutes. Turn the setting to low and slowly add in half the flour mixture, and whisk for about 30 seconds. Add the clementine juice, zest, and vanilla, then add the remaining flour mixture and whisk until smooth, about 1 minute.
In a greased and floured round 9" cake pan, pour the batter. Bang the cake pan on the counter a couple times to remove the air bubbles. Place the oven and bake for 40 minutes, or until the top of golden and the cake test comes out clean.
Remove from the oven and let it cool for about 10 minutes. Using a paring knife or butter knife, run the knife around the edge of the cake to separate the cake from the edge of the pan. Cover the cake pan with a cooling rack or large plate and flip the surface and the cake pan over together. To flip the cake rightsize up, take another cooling rack and place it on the cake. Gently hold the two racks or rack and plate together without squeezing the cake, then flip the cake over so the top is up and the bottom of the cake is on the rack.
Let the cake completely cool on the wire rack. Once completely cooled, dust powdered sugar on top and serve.