1. The problem is to simplify the expression $\sqrt[3]{-1}$.\n\n2. The cube root of a number $a$ is a number $b$ such that $b^3 = a$.\n\n3. We want to find $b$ such that $b^3 = -1$.\n\n4. Since $(-1)^3 = -1$, it follows that $\sqrt[3]{-1} = -1$.\n\n5. Therefore, the simplified value of $\sqrt[3]{-1}$ is $-1$.