How do you score a word that begins on a triple word space, ends on a double word space and uses all seven of your tiles?
Note that this is something that is impossible to pull off in a standard game as the only row/column that has both a triple word and a double word is the one with the starting space and you need 8 tiles to get from the double word space to the triple word space.
According to the Scrabble rules you would take the value of the word and multiply by by 6, and then add 50 points. (The rules don't explicitly state this due to it being impossible, but they do account for 2 doubles or 2 triples so there is no reason to think that a triple and a double would work differently)
It depends on which letters were already on the board, and which ones you added.
When you place a word in Scrabble, it must attach to existing words (except for the very first play of the game). When you add to an existing word, you score any letters that were already on the board again, but you do not score any triple or double word or letter points for the spaces underneath already-existing letters; only for spaces that you just covered up for the first time.
If you mean a situation where your own letters were used to cover up both the triple and double word spaces, then this is impossible. The only places on the board where a double and triple word score exist on the same row or column use the center space; and if you were going there as your first move, you cannot reach a triple word score with only 7 letters.
Either way, you would add 50 points to the normal word score for having used all 7 of your letters.
Ignoring the board configuration, scoring works in the following way:
For each word created or extended by the placed tiles:
- Double/triple letter multipliers under newly placed tiles are applied to the tiles.
- The score [including multipliers from (1)] for the letters in the word are added together.
- For each double/triple word multiplier under a newly placed tile in the word, the score from (2) is doubled/tripled.
- We'll call the resulting number the word score.
The word scores for each new/extended word are added together.
Finally, if all 7 tiles were used, you add 50 points.
In other words, the important point is that letter multipliers are applied first, word multipliers are applied next, and the tile bonus is applied last.
Let's have an example. Look at the following situation. The board looks like this:
The light/dark blue squares are double/triple letter. The beige/red squares are double/triple word.
Let's say you play the following word:
You'd score two words: "grenades" and "stickers". You didn't modify "aisle", so you don't score it.
Let's do "stickers" first. Ignore the double letter and double word spaces, since they've already been used up. Only tiles placed this turn activate bonus spaces.
- There are no letter multipliers.
- Add the letters together: 14.
- Apply the triple word multiplier from the S: 42.
- The word score is 42.
Now "grenades". All of the bonus tiles are new, so we apply them.
- Apply the double letter modifier to the N, making it worth 2 instead of 1.
- Add the letters together: 11
- Apply both triple word multipliers from the G and S: 99.
- The word score is 99.
To finish up:
- Add the word scores together: 141.
- Add the bonus 50 for using all 7 tiles.
The turn score is 191.
If you were playing on a board that made it possible to apply double and triple word bonuses to the same play, you just multiply the word for each one. The order doesn't matter; it'll be x3 and x2, so x6 either way around.