(-2 1/3)^-2

Let's evaluate \((-2 \frac{1}{3})^{-2}\). 1. Convert the mixed number to an improper fraction: \[ -2 \frac{1}{3} = -\left(2 + \frac{1}{3}\right) = -\frac{6}{3} - \frac{1}{3} = -\frac{7}{3} \] 2. Rewrite the expression: \[ \left(-\frac{7}{3}\right)^{-2} \] 3. Recall that \(a^{-n} = \frac{1}{a^{n}}\): \[ \left(-\frac{7}{3}\right)^{-2} = \frac{1}{\left(-\frac{7}{3}\right)^2} \] 4. Square the fraction: \[ \left(-\frac{7}{3}\right)^2 = \left(-\frac{7}{3}\right) \times \left(-\frac{7}{3}\right) = \frac{(-7) \times (-7)}{3 \times 3} = \frac{49}{9} \] 5. Take the reciprocal: \[ \frac{1}{\frac{49}{9}} = \frac{9}{49} \] **Final answer:** \[ (-2 \frac{1}{3})^{-2} = \boxed{\frac{9}{49}} \]