Simplify: \( (-27)^{-\frac{5}{3}} \)

To simplify \( (-27)^{-\frac{5}{3}} \), first consider the negative exponent. The expression can be rewritten as: \[ \frac{1}{(-27)^{\frac{5}{3}}} \] Next, we simplify \( (-27)^{\frac{5}{3}} \). The fractional exponent indicates that we take the cube root of -27 and then raise it to the 5th power. The cube root of -27 is -3, since: \[ (-3)^3 = -27 \] Now we raise -3 to the power of 5: \[ (-3)^5 = -243 \] Putting this back into our expression, we have: \[ (-27)^{-\frac{5}{3}} = \frac{1}{-243} \] Thus, the simplified result is: \[ -\frac{1}{243} \]