The term 'deeply impress' can be expressed in three different ways using the solutions from the crossword. The first solution is 'ENGRAVE, ' which means to carve or cut a design into a hard surface, usually with a chisel. The second solution is 'AWE, ' which is an emotion of admiration, fear, or reverence. The third solution is 'ETCH, ' which is a process of cutting into a hard surface with acid or a sharp tool. All three solutions are related to the idea of deeply impressing something onto a surface, either physically or emotionally.