Second, I've assumed that three times the firepower means three times the overall strength, rather than just three times the beam weapon output. Again, there is nothing much to say unless we eventually get to see more of this ship in action in future incarnation of Trek.
Although this ship design was also seen in the DS9 final episode "What You Leave Behind", special effects shots indicate that those ships are considerably larger than the original battleship. After considerable wavering I've decided to class them as a new type of ship, the Dreadnoughts. See the Comments section of that class for more details about the relationship between the two ships.
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