This is true, so much so that in many cases, sacrificing pieces of higher value for pieces of lower value end up leading us to victory
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1 knight = 1 bishop = 3 pawns
1 rook = 4.5 pawns
1 queen = 3 minor pieces = 2 rooks = 9 pawns
However, the value of the pieces is not an absolute and constant number.
A pawn on the seventh rank can be very strong and perhaps promote to a queen. A knight in the center or a rook on an open file are far more effective than their passively positioned counterparts.
G.Lisitsin described five factors which influence the relative strength of the pieces:
1) The central position of a piece
2) A safe, well protected position
3) The activity of the piece
4) Coordination with other pieces
5) The mobility of the piece