1. **Evaluate** $ (8+2)^2 \div 2(3) - (-5) $. Step 1: Calculate inside the parentheses: $8+2=10$. Step 2: Square the result: $$10^2=100$$. Step 3: Multiply $2(3)=6$. Step 4: Divide: $$100 \div 6$$. Step 5: Show cancellation: $$100 \div \cancel{6} = \frac{100}{6}$$ (simplify fraction by dividing numerator and denominator by 2): $$\frac{100}{6} = \frac{\cancel{100}^{50}}{\cancel{6}^3}$$. Step 6: So division equals $$\frac{50}{3}$$. Step 7: Subtract negative: $$\frac{50}{3} - (-5) = \frac{50}{3} + 5 = \frac{50}{3} + \frac{15}{3} = \frac{65}{3}$$. 2. **Evaluate** $ 27 \div 3^2 + (-4-5)^2 $. Step 1: Calculate exponent: $$3^2=9$$. Step 2: Divide: $$27 \div 9 = 3$$. Step 3: Calculate inside parentheses: $$-4-5 = -9$$. Step 4: Square: $$(-9)^2 = 81$$. Step 5: Add: $$3 + 81 = 84$$. 3. **Evaluate** $ 12 - (-9) + 2(16 + 2^2) $. Step 1: Calculate exponent: $$2^2 = 4$$. Step 2: Add inside parentheses: $$16 + 4 = 20$$. Step 3: Multiply: $$2 \times 20 = 40$$. Step 4: Subtract negative: $$12 - (-9) = 12 + 9 = 21$$. Step 5: Add: $$21 + 40 = 61$$. 4. **Evaluate** $ (8-1) \cdot 4^3 \quad 6(-5) + 2 $. Step 1: Calculate inside parentheses: $$8-1=7$$. Step 2: Calculate exponent: $$4^3 = 64$$. Step 3: Multiply: $$7 \times 64 = 448$$. Step 4: Multiply: $$6 \times (-5) = -30$$. Step 5: Add: $$-30 + 2 = -28$$. **Final answers:** 1. $$\frac{65}{3}$$ 2. $$84$$ 3. $$61$$ 4. $$448$$ and $$-28$$