The prince doesn't sentence Romeo to death because:
1) If Romeo didn't kill Tybalt, he would've been executed anyway
2) Tybalt would've killed Romeo if Mercutio hadn't stepped in. Mercutio died because Tybalt killed him, and Tybalt died because Romeo killed him.
3) Tybalt paid the price for killing Mercutio, and when the prince asked who would "pay" for Mercutio's death, Montague said Romeo shouldn't have to because they were good friends, and Romeo killed Tybalt to avenge Mercutio.
There is a mitigating factor. Tybalt had already participated in a street fight and killed Mercutio. That meant that Tybalt's life was forfeit, so that Romeo was just doing what the law dictated. Of course, that does not give Romeo licence to be a vigilante, which is why he is punished anyway, but it does result in the reduced sentence.
Lady Capulet is asking the Prince to sentence Romeo to death.
The Prince knows that Benvolio is a trustworthy witness, despite what Lady Capulet has to say. He knows that Tybalt was the one looking for a fight and that Romeo tried to avoid it at first. Romeo only got involved after Mercutio's death, at which time Tybalt's life was forfeit to the law anyway by the same proclamation. All of these matters go in mitigation of the sentence, which is why the Prince does not sentence Romeo to death.
The Prince banished Romeo because he has killed Juliet's cousin and they don't want to sentence him to death. So they sent him to exile, out of Verona away from his family and friends.
the prince
The Prince tried his best to be fair to Romeo. The punishment for fighting in the streets was death, but Benvolio asked the Prince to consider the fact that Tybalt had already forfeited his life by fighting with Mercutio. The Prince mitigated his sentence accordingly. Since Romeo had undeniably taken part in a street fight, it would have been unfair to let him get away scot free.
Lady Capulet is asking the Prince to sentence Romeo to death.
Tybalt's cousin Juliet asks Prince Escalus to sentence Romeo to death after he kills her cousin Tybalt.
The sentence the Prince places upon Romeo for killing Tybalt is banishment from Verona.
The Prince knows that Benvolio is a trustworthy witness, despite what Lady Capulet has to say. He knows that Tybalt was the one looking for a fight and that Romeo tried to avoid it at first. Romeo only got involved after Mercutio's death, at which time Tybalt's life was forfeit to the law anyway by the same proclamation. All of these matters go in mitigation of the sentence, which is why the Prince does not sentence Romeo to death.
The Prince banished Romeo because he has killed Juliet's cousin and they don't want to sentence him to death. So they sent him to exile, out of Verona away from his family and friends.
the prince
Montague, who acts as Romeo's advocate at the trial, argues that Tybalt had already broken the law and incurred the death penalty by killing Mercutio. Romeo was therefore only carrying out the law by punishing Tybalt. "His fault concludes but what the law should end, the life of Tybalt." The Prince has no desire to encourage vigilante justice, so he does not acquit Romeo on this plea, but only reduces his sentence from death to banishment
"All are punished"
The Prince banished Romeo because he has killed Juliet's cousin and they don't want to sentence him to death. So they sent him to exile, out of Verona away from his family and friends.
The Prince tried his best to be fair to Romeo. The punishment for fighting in the streets was death, but Benvolio asked the Prince to consider the fact that Tybalt had already forfeited his life by fighting with Mercutio. The Prince mitigated his sentence accordingly. Since Romeo had undeniably taken part in a street fight, it would have been unfair to let him get away scot free.
In Romeo and Juliet, the prince banishes Romeo from Verona to the neighboring land of Mantua. The prince banishes Romeo because he kills Tybalt (Juliet's cousin) out of his rage for Tybalt killing his friend Mercutio in a brawl. Romeo is not sentenced to death by the prince, because he killed Tybalt only to avenge his friend's death. Also, the prince only exiles Romeo, so that there is a fair sentence that can appease both the Capulets and Montagues.
Because the guy he killed had already committed a capital offence by killing Mercutio. The Montagues argue that Romeo shouldn't be punished for doing to Tybalt what the hangman was going to do anyway. The prince takes this into consideration, but only reduces Romeo's sentence, as he still shouldn't be taking the law into his own hands.