Combining power-ups helps you clear more tiles and produce bigger explosions. Here are the combinations currently in the game:

Bomb+Bomb doubles the radius of the bomb effect.

Bomb+Rocket removes three rows and columns of pieces.

Rocket+Rocket removes one row and one column of tiles regardless of which way they are pointed.

Bomb or Rocket + Paper Plane makes the Paper Plane take the Bomb or Rocket along with it to a random tile.

Plane+Plane produces three Paper Planes that target different tiles.

Rainbow Ball + Rocket/Bomb/Plane makes the Rainbow Ball turn all the pieces of one type (the one currently the most common on the field) into respective power-ups.

Rainbow Ball+Rainbow Ball removes all pieces from the field, clearing one obstacle layer in the process.