the task: Identify the errors a stundent made in the following problems and correct them. Explain your answer.
1. (7x)^1/3 = 1 divided by 7x^3
my answer: it should be = (7x)^1/3 = 7^1/3 x^1/3
Is that right?
2. 2^2 divided by 2^1/4 = 2^2/4 = 2^1/2 = square root of 2
What is wrong? I have an idea, but I am not sure.
Re: Identify errors
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)