how is the 5th root of -32 an integer? In the solution video, Greg says that the answer is -2.
But isn’t the 5th root of -32 an imaginary number?
There are 5 solutions to \sqrt[5]{-32}, and 4 of them are complex solutions. However, since we’re working strictly on \mathbb{R} and not \mathbb{C}, we’re only interested in the real solutions.
For the real solution, it is easy to see that:
(-2)^5 = (-2) \cdot (-2) \cdot (-2) \cdot (-2) \cdot (-2) = -32.