1. Problem: Evaluate $$[25 - 3(6+1)] \div 4 + 9$$. Step 1: Calculate inside the parentheses: $$6+1=7$$. Step 2: Multiply: $$3 \times 7 = 21$$. Step 3: Subtract: $$25 - 21 = 4$$. Step 4: Divide: $$4 \div 4=1$$. Step 5: Add: $$1 + 9 = 10$$. 2. Problem: Evaluate $$180 \div 15 \times \{(12-6) - (14-12)\}$$. Step 1: Calculate parentheses: $$12-6=6$$ and $$14-12=2$$. Step 2: Subtract inside braces: $$6 - 2 = 4$$. Step 3: Divide: $$180 \div 15=12$$. Step 4: Multiply: $$12 \times 4 = 48$$. 3. Problem: Evaluate $$3 + 2^4 \times (15 \div 3)$$. Step 1: Exponent: $$2^4=16$$. Step 2: Divide: $$15 \div 3=5$$. Step 3: Multiply: $$16 \times 5=80$$. Step 4: Add: $$3 + 80=83$$. 4. Problem: Evaluate $$48 \div 2 \times (9 - 7) + 6$$. Step 1: Parentheses: $$9-7=2$$. Step 2: Divide: $$48 \div 2=24$$. Step 3: Multiply: $$24 \times 2=48$$. Step 4: Add: $$48 + 6=54$$. 5. Problem: Evaluate $$36 \times 2 \div (4 + 2) + 5$$. Step 1: Parentheses: $$4 + 2=6$$. Step 2: Multiply: $$36 \times 2=72$$. Step 3: Divide: $$72 \div 6=12$$. Step 4: Add: $$12 + 5=17$$. 6. Problem: Evaluate $$\{50 - (2+3) + 15\}$$. Step 1: Parentheses: $$2+3=5$$. Step 2: Subtract: $$50 - 5 = 45$$. Step 3: Add: $$45 + 15=60$$. 7. Problem: Evaluate $$[18 - 2(5+1)] \div 3 + 7$$. Step 1: Parentheses: $$5+1=6$$. Step 2: Multiply: $$2 \times 6=12$$. Step 3: Subtract: $$18 - 12=6$$. Step 4: Divide: $$6 \div 3=2$$. Step 5: Add: $$2 + 7=9$$. 8. Problem: Evaluate $$6 + 6 \times 2 - 3^2$$. Step 1: Exponent: $$3^2=9$$. Step 2: Multiply: $$6 \times 2=12$$. Step 3: Add and subtract: $$6 + 12 - 9 = 9$$. 9. Problem: Evaluate $$4^2 - (2 + 6) \div 2 + 5$$. Step 1: Exponent: $$4^2=16$$. Step 2: Parentheses: $$2 + 6=8$$. Step 3: Divide: $$8 \div 2=4$$. Step 4: Calculate: $$16 - 4 + 5 = 17$$. 10. Problem: Evaluate $$15 - \{3 \times (4 - 2)\} + 2^3$$. Step 1: Parentheses: $$4 - 2 = 2$$. Step 2: Multiply: $$3 \times 2 = 6$$. Step 3: Exponent: $$2^3=8$$. Step 4: Calculate: $$15 - 6 + 8 = 17$$. 11. Problem: Evaluate $$12 \div 2 + (4^2 - 2^3) \times 3$$. Step 1: Divide: $$12 \div 2 = 6$$. Step 2: Exponents: $$4^2=16$$, $$2^3=8$$. Step 3: Parentheses: $$16 - 8 = 8$$. Step 4: Multiply: $$8 \times 3=24$$. Step 5: Add: $$6 + 24 = 30$$. 12. Problem: Evaluate $$24 \div (3 \times 2) + \{7 - (3 + 1)^2\} + 5^0$$. Step 1: Multiply: $$3 \times 2=6$$. Step 2: Divide: $$24 \div 6=4$$. Step 3: Parentheses: $$3 + 1=4$$. Step 4: Exponent: $$4^2=16$$. Step 5: Subtract: $$7 - 16 = -9$$. Step 6: Exponent: $$5^0=1$$. Step 7: Calculate: $$4 + (-9) + 1 = -4$$. 13. Problem: Evaluate $$(15 - 3^2) + \{6 \div (1+1)\}^2 - 4$$. Step 1: Exponent: $$3^2=9$$. Step 2: Subtract: $$15 - 9=6$$. Step 3: Parentheses: $$1 + 1=2$$. Step 4: Divide: $$6 \div 2=3$$. Step 5: Square: $$3^2=9$$. Step 6: Final calculation: $$6 + 9 - 4 = 11$$. 14. Problem: Evaluate $$2^3 \times (3+5) - \sqrt{64 + 8/2}$$. Step 1: Exponent: $$2^3=8$$. Step 2: Parentheses: $$3 + 5=8$$. Step 3: Multiply: $$8 \times 8=64$$. Step 4: Divide inside root: $$8/2=4$$. Step 5: Add inside root: $$64 + 4=68$$. Step 6: Square root: $$\sqrt{68} = 2\sqrt{17}$$ (approx 8.246). Step 7: Subtract: $$64 - 8.246 \approx 55.754$$. 15. Problem: Evaluate $$\frac{(5^2 - 3^2) + 12}{2^2 + 1} + \frac{9}{3}$$. Step 1: Exponents: $$5^2=25$$, $$3^2=9$$, $$2^2=4$$. Step 2: Subtract: $$25 - 9 =16$$. Step 3: Sum numerator: $$16 + 12=28$$. Step 4: Sum denominator: $$4 + 1=5$$. Step 5: Divide numerator/denominator: $$28 \div 5=5.6$$. Step 6: Divide: $$9 \div 3=3$$. Step 7: Add: $$5.6 + 3=8.6$$. 16. Problem: Evaluate $$2^3 + 5 \times \{6 - 2 \times [3 + (4 - 2)^2]\}$$. Step 1: Parentheses inner: $$4 - 2=2$$. Step 2: Exponent: $$2^2=4$$. Step 3: Square bracket: $$3 + 4 = 7$$. Step 4: Multiply inside braces: $$2 \times 7 =14$$. Step 5: Subtract: $$6 - 14 = -8$$. Step 6: Multiply: $$5 \times (-8) = -40$$. Step 7: Exponent: $$2^3=8$$. Step 8: Add: $$8 + (-40) = -32$$. 17. Problem: Evaluate $$12 \times (6 + \frac{3^2 + 4}{2}) - 7^2$$. Step 1: Exponent: $$3^2=9$$. Step 2: Add numerator: $$9 + 4=13$$. Step 3: Divide: $$13 \div 2=6.5$$. Step 4: Add inside parentheses: $$6 + 6.5=12.5$$. Step 5: Multiply: $$12 \times 12.5=150$$. Step 6: Exponent: $$7^2=49$$. Step 7: Subtract: $$150 - 49=101$$. 18. Problem: Evaluate $$8 \times 3 + \left[\frac{63}{\frac{18}{3} \times (9 - 17 + 5 \times 2)}\right]$$. Step 1: Multiply: $$8 \times 3=24$$. Step 2: Divide: $$18 \div 3=6$$. Step 3: Multiply inside parentheses: $$5 \times 2=10$$. Step 4: Sum inside parentheses: $$9 - 17 + 10 = 2$$. Step 5: Multiply denominator: $$6 \times 2=12$$. Step 6: Divide fraction: $$63 \div 12=5.25$$. Step 7: Add: $$24 + 5.25=29.25$$. 19. Problem: Evaluate $$\frac{2^4 + 6 \times (2 + 3)}{3^2 -1} + \left(\frac{1}{2} \times 8\right) - 3$$. Step 1: Exponents: $$2^4=16$$, $$3^2=9$$. Step 2: Parentheses sum: $$2 + 3=5$$. Step 3: Multiply: $$6 \times 5=30$$. Step 4: Numerator: $$16 + 30=46$$. Step 5: Denominator: $$9 -1=8$$. Step 6: Divide fraction: $$46 \div 8 = 5.75$$. Step 7: Multiply second term: $$\frac{1}{2} \times 8=4$$. Step 8: Calculate result: $$5.75 + 4 - 3 = 6.75$$. 20. Problem: Evaluate $$[2^3 \times \{4 + 6 \div (1+2)\}] - \sqrt{64} + 9 \div 3$$. Step 1: Exponents: $$2^3=8$$. Step 2: Parentheses: $$1 + 2 = 3$$. Step 3: Divide inside braces: $$6 \div 3=2$$. Step 4: Add inside braces: $$4 + 2=6$$. Step 5: Multiply: $$8 \times 6=48$$. Step 6: Square root: $$\sqrt{64}=8$$. Step 7: Divide: $$9 \div 3=3$$. Step 8: Calculate: $$48 - 8 + 3 = 43$$. 21. Problem: Evaluate $$\left(\frac{5}{2} \times \frac{3}{4}\right) - \left(\frac{8}{3^2 + 1^3}\right) + \frac{1}{\sqrt{16}}$$. Step 1: Multiply fractions: $$\frac{5}{2} \times \frac{3}{4} = \frac{15}{8} = 1.875$$. Step 2: Calculate denominator: $$3^2=9$$, $$1^3=1$$, sum $$9 + 1 = 10$$. Step 3: Divide: $$\frac{8}{10} = 0.8$$. Step 4: Square root: $$\sqrt{16} = 4$$. Step 5: Divide: $$\frac{1}{4} = 0.25$$. Step 6: Sum all: $$1.875 - 0.8 + 0.25 = 1.325$$. 22. Problem: Find the value of $$a$$ if $$42 \div 2 + a \times 3 - 22 = 8$$. Step 1: Divide: $$42 \div 2 = 21$$. Step 2: Set up equation: $$21 + 3a - 22 = 8$$. Step 3: Simplify: $$-1 + 3a = 8$$. Step 4: Add 1 to both sides: $$3a = 9$$. Step 5: Divide both sides by 3: $$a = 3$$.