1. The problem is to simplify the expression $-27^{1/3}$. 2. The expression involves a negative sign and a cube root. The cube root of a number $a$ is written as $a^{1/3}$. 3. According to order of operations, exponents are evaluated before the negative sign. So we first calculate $27^{1/3}$. 4. The cube root of 27 is the number which when cubed gives 27. Since $3^3 = 27$, we have $27^{1/3} = 3$. 5. Now apply the negative sign: $-27^{1/3} = -3$. 6. Therefore, the simplified value of $-27^{1/3}$ is $-3$.