Question

I'm not sure how to answer b.

Answer 1

If you want to check whether a cube root is correct, simply cube your solution and see if you get back the number under the radical. In this case, we can check that $\sqrt[3]{-512} =-8$ by cubing -8, getting us

$(-8)^3=(-8)\cdot(-8)\cdot(-8)=64\cdot(-8)=-512$

Our check checks out!