For (1) remember that a^(1/b) is equal to the bth root of a, whereas a^(-b) = 1/a^b. So while (7x)^(1/3) is indeed equal to 7^(1/3) x^(1/3), this doesn't explain what the error was. The student is wrong because 1 divided by 7x^3 = (7x)^(-3), not (7x)^(1/3).

For (2), when you divide a^b by a^c you get a^(b-c). So 2^2 divided by 2^(1/4) = 2^(2-1/4) = 2^(7/4)