How do you simplify (-y^ 3)^6?

The answer is ${y}^{18}$.
${\left(- {y}^{3}\right)}^{6} = - {y}^{3 \cdot 6} = {y}^{18}$
Because $- {y}^{3}$ is multiplied times itself six times, an even number, it becomes positive.
$- {y}^{3} \cdot - {y}^{3} \cdot - {y}^{3} \cdot - {y}^{3} \cdot - {y}^{3} \cdot - {y}^{3} = {y}^{18}$.