Let's break down the cuts step by step, starting with one board:
- First cut: The carpenter cuts the board in half. So now we have 2 pieces.
- Second cut: Each of those 2 pieces is cut in half again. So now we have 2 pieces x 2 = 4 pieces.
- Third cut: Each of those 4 pieces is cut in half again. So now we have 4 pieces x 2 = 8 pieces.
So after three rounds of cuts, the total number of pieces of wood is 8 pieces.