I have a little question concerning negative roots. I just happened to be doing an exercise which required taking the fifth root of (-32). I thought that one cannot take a root out of a negative number if the answer is supposed to belong to the real numbers. However is it so one cannot take the square root of a negative number, and any other even root(e.g fourth root, sixth root), but one can take roots of negative numbers if the root is negative(e.g cube root)?
that's because they are two different things. they are not equal.
on the left you have while on the right you have . they are not the same thing. the first is not a real number, the second is a negative number
watch your parentheses. do you understand the difference between the two?