1. **State the problem:** Simplify the expression $$\left(-\frac{2}{3} + \frac{1}{6}\right)^2 \div \frac{5}{4}$$ and express the answer as a simplified fraction. 2. **Add the fractions inside the parentheses:** $$-\frac{2}{3} + \frac{1}{6}$$ To add, find a common denominator, which is 6. $$-\frac{2}{3} = -\frac{4}{6}$$ So, $$-\frac{4}{6} + \frac{1}{6} = -\frac{3}{6} = -\frac{1}{2}$$ 3. **Square the result:** $$\left(-\frac{1}{2}\right)^2 = \frac{1}{4}$$ 4. **Divide by $$\frac{5}{4}$$:** Dividing by a fraction is the same as multiplying by its reciprocal. $$\frac{1}{4} \div \frac{5}{4} = \frac{1}{4} \times \frac{4}{5} = \frac{1 \times 4}{4 \times 5} = \frac{4}{20}$$ 5. **Simplify the fraction:** $$\frac{4}{20} = \frac{1}{5}$$ **Final answer:** $$\frac{1}{5}$$