Does Hashem (keva'Yachol) have two Right Hands?
Rashi #1: The Torah is merely hinting here that when Yisrael do the will of Hashem, then His Left Hand (Midas ha'Din) turns into a Right Hand 1 (Midas Rachamim). Consequently, one Right Hand saves Yisrael while the other one crushes the enemy. 2
Rashi #2: With the same Right Hand with which Hashem saved Yisrael, He crushed the Egyptians - a feat which no human being is able to emulate.
Rashi #3 and Rashbam: The Pasuk is saying that Hashem's Right Hand (which is mighty), that Right Hand crushes the enemy. 3
Ramban #1 (citing Ibn Ezra): "Your Right Hand, Hashem, who is mighty ("Ne'dari" - masculine) in strength, Your Right Hand crushes ("Tir'atz" - feminine) the enemy." 4
Ramban #2: "Your Right Hand Hashem, is mighty in strength, to humiliate whoever is arrogant and haughty. 5
Seforno: The Torah is stressing here that it is Hashem's Right Hand that is powerful; and not that of Pharaoh's army and elite troops, who rely on the might of their arms.
Hadar Zekenim: However. when they transgress His will, His Right Hand turns into a left hand.
The (stronger) right Hand, destroys the enemy - implying that even Hashem's Midas Rachamim agrees that they need to be destroyed.
Rashi and Rashbam: And it is the way of the Torah to repeat a key word or phrase in this way, as we find on numerous occasions. See for example Tehilim 92:10, Tehilim 94:3, Tehilim 93:3. But see Ramban's objection to this explanation.
Simultaneously describing Hashem's Right Hand in the masculine and in the feminine.
What is the significance of the extra 'Yud' in "Ne'dari"?
Rashi, Da'as Zekenim and Hadar Zekenim: It is common for the Torah to add a 'Yud' on to an adjective in this way. 1
See for example Eichah 1:1, Bereishis 31:39 (Rashi) and Tehilim 123:1 (Da'as Zekenim).
How will we reconcile the words "Ne'dari ba'Ko'ach," with the Pasuk in Iyov, "Shakai Lo Metzanu'hu Sagi Ko'ach" (Iyov 37:23)?
Avodah Zarah 4a: Whereas the current Pasuk is referring to a time of war, the Pasuk in Iyov is referring to when Hashem sits in judgment. 1
Torah Temimah: Because if Hashem would apply the full force of the Din, no one would survive.
How is this Pasuk a continuation of the idea expressed in the preceding one?
Maharal (Gevuros Hashem Ch. 47, p. 190): In 15:5, we described how Hashem struck the Egyptians a mighty blow. In human battle, the more intensely one strikes at the enemy, the more likely it is that the repercussions of that strike will hit one's own soldiers as well. But here, Hashem was in full control. As the Mechilta 1 illustrates - Hashem's 'one hand' was saving Yisrael, and the other was simultaneously drowning the Egyptians in the sea.
Rashi also expresses this idea.
QUESTIONS ON RASHI
Rashi writes: "'Tir'atz Oyev - [I.e.], it always breaks and shatters the enemy." What is bothering Rashi?
Gur Aryeh: Why is the verb "Tir'atz" in future tense? We would expect it to be in past tense, as are most verbs in the Shirah, 1 describing the miracles that Hashem had just done. But as Rashi (to 15:1) explained above, when describing something that takes place constantly, either past or future tense may be used. 2