Your notation is all wrong. I'm assuming you mean c^(m/n) and I also assume the n is an index of the radical (e.g. n = 2 would be a square root, n = 3 would be a cube root, n = 4 would be a fourth root, etc.)

However, I believe the answer is intended to be true.

Answer:

a. True

It's actually false.

The problem is that the rational powers of negative numbers are very badly behaved. The most common counterexample is c=-1 and m=n=2.

True

Your notation SUCKS so I am not sure what you mean by any of that

for clarity, did you mean:

c^(m/n) = nth root of (c^m) = (nth root of c)^m --?

If so, then it's true.

*nth root of x = x^(1/n)

a. True