1) To solve the equation √x^6 = -x^3, we can rewrite it as x^3 = -x^3. Then, we can solve for x by taking the cube root of both sides:

x = -1

Therefore, the solution to the equation √x^6 = -x^3 is x = -1.

2) To solve the equation √c^4 = -c^2, we can rewrite it as c^2 = -c^2. Then, we can solve for c by taking the square root of both sides:

c = imaginary number (√1)c = ± i

Therefore, the solution to the equation √c^4 = -c^2 is c = ± i.