What is the difference between "u'Shemartem" and "va'Asisem"?
Rashi: The former refers to Mishnah - learning; the latter, to carrying out what one learned.
Tzror ha'Mor Ekev (DH v'Hayah): "U'Shemartem" is to avoid transgressing Lavim; "Va'Asisem" corresponds to Mitzvos Aseh.
Targum Onkelos and Targum Yonasan: They refer to guarding (keeping in mind) the Torah and doing what it says.
What is "Hi" referring to?
Rashi: It is referring to the learning and the carrying out mentioned earlier in the Pasuk. 1
Targum Onkelos and Yonasan: It is referring to the Torah, which "u'Shemartem va'Asisem" themselves are referring to.
Rashi: And it is as if it says 'through the learning mentioned earlier, you will be considered wise men
What are the connotations of "Ki Hi Chochmaschem ... le'Einei ha'Amim"?
Rashi: It is through the study of Torah and its observance that we are considered wise and understanding in the eyes of the nations.
Seforno: It is by means of the Torah that we are able to answer the Apikorsim with logical arguments. 1
Shabbos 75a: It refers to the calculation of Tekufos (solstices and equinoxes) and Mazalos (the times and positions of the constellations).
Why is it important to be considered wise in the eyes of the nations?
Seforno: Because, as the Torah goes on to explain, Hashem is close to us inasmuch as He answers us when we call to Him, a clear proof that He chose us from all the nations, and it would be a Chilul Hashem if the nations would consider us foolish.