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Good question! I didn't do a good job at explaining power-ups. There was only one line of text on the first wave about it.
The power-ups are collectibles, and there is a counter on the top of the screen for how many you have. The more power-ups you have, the stronger your "push" force-field gets (it pushes bullets away faster). When you die, you lose all your power-ups. Each level spawns at least 1 power-up.