Preheat oven to 350 degrees Fahrenheit (175 degrees Celsius) and grease a 9x13 inch baking pan.
In a large mixing bowl, whisk together flour, sugar, baking powder, baking soda, cinnamon, nutmeg, and salt.
In a separate medium bowl, beat the mashed sweet potatoes, vegetable oil, eggs, and vanilla extract until well combined.
Add the dry ingredients to the wet mixture and stir until just incorporated, ensuring no large lumps remain.
Transfer the batter into the prepared baking pan and level the surface with a spatula.
Bake for 40 to 45 minutes, or until a wooden skewer inserted into the center comes out clean.
Remove from oven and allow the cake to cool completely in the pan on a wire rack.