1. We are asked to evaluate several arithmetic expressions step-by-step. 2. Expression a) $$4\times 3 + 8$$ - Calculate multiplication: $$4\times 3 = 12$$ - Add 8: $$12 + 8 = 20$$ 3. Expression b) $$(9 - 2) + (3^2 \times 21)$$ - Calculate inside parentheses: $$9 - 2 = 7$$ - Calculate exponent: $$3^2 = 9$$ - Multiply: $$9 \times 21 = 189$$ - Add: $$7 + 189 = 196$$ 4. Expression c) $$84 \div 3 \times 4$$ - Divide: $$84 \div 3 = 28$$ - Multiply: $$28 \times 4 = 112$$ 5. Expression d) $$8(2 + 5) \div [25 - (7 \times 3)]$$ - Calculate inside parentheses: $$2 + 5 = 7$$ - Calculate multiplication: $$7 \times 3 = 21$$ - Subtract inside brackets: $$25 - 21 = 4$$ - Multiply: $$8 \times 7 = 56$$ - Divide: $$56 \div 4 = 14$$ 6. Expression e) $$(18 + 14) \div (6 + 2)$$ - Add numerator: $$18 + 14 = 32$$ - Add denominator: $$6 + 2 = 8$$ - Divide: $$32 \div 8 = 4$$ 7. Expression f) $$7 + [2(12 - 5)+ 32] - 18 \div 3$$ - Calculate parentheses: $$12 - 5 = 7$$ - Multiply: $$2 \times 7 = 14$$ - Add inside brackets: $$14 + 32 = 46$$ - Divide: $$18 \div 3 = 6$$ - Add and subtract: $$7 + 46 - 6 = 47$$ 8. Expression g) $$53 + 7 - 30$$ - Add: $$53 + 7 = 60$$ - Subtract: $$60 - 30 = 30$$ 9. Expression h) $$6 + (2 \times 7 + 5^2)$$ - Multiply: $$2 \times 7 = 14$$ - Calculate exponent: $$5^2 = 25$$ - Add inside parentheses: $$14 + 25 = 39$$ - Add: $$6 + 39 = 45$$ 10. Expression i) $$(16 + 82) \div (4 - 2)$$ - Add numerator: $$16 + 82 = 98$$ - Subtract denominator: $$4 - 2 = 2$$ - Divide: $$98 \div 2 = 49$$ 11. Expression j) $$5 \left[ 64 \div 2^3 (20 - 10) - 5 \right]$$ - Calculate exponent: $$2^3 = 8$$ - Calculate parentheses: $$20 - 10 = 10$$ - Divide: $$64 \div 8 = 8$$ - Multiply: $$8 \times 10 = 80$$ - Subtract inside brackets: $$80 - 5 = 75$$ - Multiply outside brackets: $$5 \times 75 = 375$$ Final answers: a) 20 b) 196 c) 112 d) 14 e) 4 f) 47 g) 30 h) 45 i) 49 j) 375