1. Problem: Evaluate each expression in Q3(a). 2. Use order of operations (PEMDAS): Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). 3. Evaluate Q3(a): $7 \times 4 - 3$ $$7 \times 4 = 28$$ $$28 - 3 = 25$$ 4. Evaluate Q3(b): $2 \times 8 + 3$ $$2 \times 8 = 16$$ $$16 + 3 = 19$$ 5. Evaluate Q3(c): $1 \times 6 + 5 \times 2$ $$1 \times 6 = 6$$ $$5 \times 2 = 10$$ $$6 + 10 = 16$$ 6. Evaluate Q3(d): $2 \times 5 + 8 \div 4$ $$2 \times 5 = 10$$ $$8 \div 4 = 2$$ $$10 + 2 = 12$$ 7. Evaluate Q3(e): $3 + (4 + 2)^2$ $$4 + 2 = 6$$ $$(6)^2 = 36$$ $$3 + 36 = 39$$ 8. Evaluate Q3(f): $(3 - 2) + (7 - 4)^2$ $$3 - 2 = 1$$ $$7 - 4 = 3$$ $$(3)^2 = 9$$ $$1 + 9 = 10$$ 9. Evaluate Q3(g): $2 \times (3^2 - 1)^2 + 3 \times (7 - 8)$ $$3^2 = 9$$ $$9 - 1 = 8$$ $$(8)^2 = 64$$ $$2 \times 64 = 128$$ $$7 - 8 = -1$$ $$3 \times (-1) = -3$$ $$128 + (-3) = 125$$ 10. Evaluate Q3(h): $7 + (4^2 - 6)^3 - 6^2$ $$4^2 = 16$$ $$16 - 6 = 10$$ $$(10)^3 = 1000$$ $$6^2 = 36$$ $$7 + 1000 - 36 = 971$$ 11. Evaluate Q3(i): $(3 + 2) [6 - 4(3^2 - 2^3)]$ $$3 + 2 = 5$$ $$3^2 = 9$$ $$2^3 = 8$$ $$9 - 8 = 1$$ $$4 \times 1 = 4$$ $$6 - 4 = 2$$ $$5 \times 2 = 10$$ 12. Evaluate Q3(j): $5 + 3 [7 + 8 \{6 - 2)^2 + 5^3\}]$ Note: There is a likely typo in the problem: "8 {6 - 2)² + 5³}". Assuming it means $8 \times (6 - 2)^2 + 5^3$. $$6 - 2 = 4$$ $$(4)^2 = 16$$ $$8 \times 16 = 128$$ $$5^3 = 125$$ $$128 + 125 = 253$$ $$7 + 253 = 260$$ $$3 \times 260 = 780$$ $$5 + 780 = 785$$ 13. Evaluate Q3(k): $10 - 8 [(7 + 4) - 6 (7 - 3)^2 - (9 - 7)^3]$ $$7 + 4 = 11$$ $$7 - 3 = 4$$ $$(4)^2 = 16$$ $$6 \times 16 = 96$$ $$9 - 7 = 2$$ $$(2)^3 = 8$$ $$11 - 96 - 8 = 11 - 104 = -93$$ $$8 \times (-93) = -744$$ $$10 - (-744) = 10 + 744 = 754$$ 14. Evaluate Q3(l): $(12 - 10) [(7 - 4) \{8 (2 - 5) - 14 (-3) + 7\}]$ $$12 - 10 = 2$$ $$7 - 4 = 3$$ $$2 - 5 = -3$$ $$8 \times (-3) = -24$$ $$-14 \times (-3) = 42$$ $$-24 + 42 + 7 = 25$$ $$3 \times 25 = 75$$ $$2 \times 75 = 150$$ Final answers for Q3: (a) 25 (b) 19 (c) 16 (d) 12 (e) 39 (f) 10 (g) 125 (h) 971 (i) 10 (j) 785 (k) 754 (l) 150 --- 15. Problem: Simplify expressions using rules of indices in Q4(a). 16. Rules: When multiplying powers with the same base, add exponents: $x^a \times x^b = x^{a+b}$. When dividing powers with the same base, subtract exponents: $\frac{x^a}{x^b} = x^{a-b}$. Any number to the zero power is 1: $x^0 = 1$. Negative exponents mean reciprocal: $x^{-a} = \frac{1}{x^a}$. 17. Simplify Q4(a): $x^2 \times x^7 \times x^{-1}$ $$x^{2+7-1} = x^{8}$$ 18. Simplify Q4(b): $x^{-2} \times x^{-3} \times x^{-4}$ $$x^{-2-3-4} = x^{-9} = \frac{1}{x^9}$$ 19. Simplify Q4(c): $\frac{1}{x^3} \times \frac{1}{x^{-6}}$ Rewrite as $x^{-3} \times x^{6} = x^{-3+6} = x^{3}$ 20. Simplify Q4(d): $\frac{1}{x^0} \times x^8 \times x^{-2}$ Since $x^0 = 1$, this is $1 \times x^{8-2} = x^{6}$ 21. Simplify Q4(e): $\frac{x^{12}}{x^4} = x^{12-4} = x^{8}$ 22. Simplify Q4(f): $\frac{x^7}{x^5} = x^{7-5} = x^{2}$ 23. Simplify Q4(g): $\frac{x^{-10}}{x^{-3}} = x^{-10 - (-3)} = x^{-7} = \frac{1}{x^7}$ 24. Simplify Q4(h): $\frac{x^{10}}{x^{-6}} = x^{10 - (-6)} = x^{16}$ 25. Simplify Q4(i): $(xy)^4 (xy)^2 = (xy)^{4+2} = (xy)^6 = x^6 y^6$ 26. Simplify Q4(j): $(x^2 y)^4 (x^3 y^2)^5$ $$= x^{2 \times 4} y^{1 \times 4} \times x^{3 \times 5} y^{2 \times 5} = x^{8} y^{4} \times x^{15} y^{10} = x^{8+15} y^{4+10} = x^{23} y^{14}$$ 27. Simplify Q4(k): $\sqrt{x} \times \sqrt[3]{x} = x^{\frac{1}{2}} \times x^{\frac{1}{3}} = x^{\frac{1}{2} + \frac{1}{3}} = x^{\frac{3}{6} + \frac{2}{6}} = x^{\frac{5}{6}}$ 28. Simplify Q4(l): $\sqrt[3]{x^2} \times \sqrt[4]{x^2} = x^{\frac{2}{3}} \times x^{\frac{2}{4}} = x^{\frac{2}{3} + \frac{1}{2}} = x^{\frac{4}{6} + \frac{3}{6}} = x^{\frac{7}{6}}$ Final answers for Q4: (a) $x^{8}$ (b) $\frac{1}{x^{9}}$ (c) $x^{3}$ (d) $x^{6}$ (e) $x^{8}$ (f) $x^{2}$ (g) $\frac{1}{x^{7}}$ (h) $x^{16}$ (i) $x^{6} y^{6}$ (j) $x^{23} y^{14}$ (k) $x^{\frac{5}{6}}$ (l) $x^{\frac{7}{6}}$