1. The problem is to simplify the expression: $(2) -1 - (-3)^2 = -1 - (81) \times (-8)^2$. 2. First, evaluate the powers: $$(-3)^2 = 9$$ $$(-8)^2 = 64$$ 3. Substitute these values back into the expression: $$2 - 1 - 9 = -1 - 81 \times 64$$ 4. Simplify the left side: $$2 - 1 - 9 = 1 - 9 = -8$$ 5. Calculate the multiplication on the right side: $$81 \times 64 = 5184$$ 6. Now the expression is: $$-8 = -1 - 5184$$ 7. Simplify the right side: $$-1 - 5184 = -5185$$ 8. The equation becomes: $$-8 = -5185$$ This is not true, so the original expression is not an equation but a simplification task. The simplified left side is $-8$, and the right side is $-5185$. Since the original expression is ambiguous, if the goal is to simplify the left side only: $$2 - 1 - (-3)^2 = 2 - 1 - 9 = -8$$ Therefore, the simplified value of the first expression is $-8$. --- For the second expression: $(3) -3 \frac{1}{6} - (-1 \frac{1}{2})^2 = -1 \frac{5}{6}$ 1. Convert mixed numbers to improper fractions: $$-3 \frac{1}{6} = -\frac{19}{6}$$ $$-1 \frac{1}{2} = -\frac{3}{2}$$ 2. Square the second term: $$\left(-\frac{3}{2}\right)^2 = \frac{9}{4}$$ 3. Substitute back: $$-\frac{19}{6} - \frac{9}{4}$$ 4. Find common denominator (12): $$-\frac{19}{6} = -\frac{38}{12}$$ $$\frac{9}{4} = \frac{27}{12}$$ 5. Perform subtraction: $$-\frac{38}{12} - \frac{27}{12} = -\frac{65}{12}$$ 6. Convert back to mixed number: $$-\frac{65}{12} = -5 \frac{5}{12}$$ The given answer $-1 \frac{5}{6}$ does not match this calculation, so please verify the original problem. --- Final answer for the first problem: $-8$.