{
  "title": "Laws of Exponents (Indices) - Grade 9 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Simplify: 2³ × 2² = ? ✏️", "options": {"A": "2⁵", "B": "2⁶", "C": "4⁵", "D": "2¹"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "What is (5²) ÷ (5¹)? 🧮", "options": {"A": "5³", "B": "5", "C": "1", "D": "25"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "Solve: a⁴ × a⁵ = ? 📚", "options": {"A": "a⁹", "B": "a²⁰", "C": "a", "D": "2a⁹"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "Simplify: (3²)³ = ? 🔢", "options": {"A": "3⁵", "B": "9⁶", "C": "3⁶", "D": "3⁸"}, "correct_answer": "C"},
    {"id": 5, "difficulty": "easy", "question": "What is 7⁰? 🤔", "options": {"A": "7", "B": "0", "C": "1", "D": "70"}, "correct_answer": "C"},
    {"id": 6, "difficulty": "easy", "question": "Calculate: 10⁵ ÷ 10³ = ? ⚡", "options": {"A": "10²", "B": "10⁸", "C": "100⁰", "D": "10¹⁵"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "Simplify: x⁷ ÷ x⁴ = ? ✨", "options": {"A": "x³", "B": "x¹¹", "C": "x²⁸", "D": "1"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "Find: (2 × 3)² = ? 🎯", "options": {"A": "6²", "B": "2² × 3", "C": "2² + 3²", "D": "13"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "Solve: 4³ × 4⁰ = ? 💡", "options": {"A": "4³", "B": "0", "C": "1", "D": "12"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "What is (y²)⁴? 🧠", "options": {"A": "y⁶", "B": "y⁸", "C": "2y⁸", "D": "y²"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "Simplify: 6⁵ ÷ 6² = ? 📐", "options": {"A": "6³", "B": "6⁷", "C": "6¹⁰", "D": "36"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "Calculate: (1⁰⁰)²² = ? 😄", "options": {"A": "0", "B": "1", "C": "100", "D": "222"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "If p⁴ × p = pⁿ, what is n? 🔍", "options": {"A": "3", "B": "4", "C": "5", "D": "1"}, "correct_answer": "C"},
    {"id": 14, "difficulty": "easy", "question": "Simplify: (5³) ÷ (5³) = ? ➗", "options": {"A": "0", "B": "5⁶", "C": "1", "D": "5⁹"}, "correct_answer": "C"},
    {"id": 15, "difficulty": "easy", "question": "What is 8¹? 👶", "options": {"A": "0", "B": "1", "C": "8", "D": "80"}, "correct_answer": "C"},
    {"id": 16, "difficulty": "easy", "question": "Find: m⁸ ÷ m⁸ = ? ⚖️", "options": {"A": "m⁰", "B": "0", "C": "1", "D": "m¹⁶"}, "correct_answer": "C"},
    {"id": 17, "difficulty": "easy", "question": "Simplify: 9² × 9³ = ? 🚀", "options": {"A": "9⁵", "B": "9⁶", "C": "81⁵", "D": "18⁵"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "Solve: (z⁵)² = ? 🧩", "options": {"A": "z⁷", "B": "z¹⁰", "C": "z²⁵", "D": "2z⁵"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "What is 2⁴ ÷ 2²? ✂️", "options": {"A": "2²", "B": "2⁶", "C": "2⁸", "D": "1"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "Simplify: k³ × k⁶ = ? 🎈", "options": {"A": "k⁹", "B": "k¹⁸", "C": "2k⁹", "D": "k³"}, "correct_answer": "A"},
    {"id": 21, "difficulty": "medium", "question": "Simplify: (2a²b)³ = ? ⚗️", "options": {"A": "6a⁵b³", "B": "8a⁶b³", "C": "2a⁶b³", "D": "8a⁵b³"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "Find x if (3ˣ)² = 3¹². 🔎", "options": {"A": "4", "B": "6", "C": "10", "D": "24"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "Simplify: (-4)³ × (-4)² = ? ❄️", "options": {"A": "(-4)⁵", "B": "(-4)⁶", "C": "16⁵", "D": "-1024"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "If 5ᵐ ÷ 5³ = 5⁵, what is m? 🧮", "options": {"A": "2", "B": "8", "C": "15", "D": "125"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "medium", "question": "Simplify: (x⁴y²)/(x²y) = ? 🌿", "options": {"A": "x²y", "B": "x⁶y³", "C": "x²y²", "D": "x⁸y²"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "Express 2⁷ × 8² as a power of 2. 🧱", "options": {"A": "2¹¹", "B": "2¹³", "C": "2⁹", "D": "2¹⁰"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "Simplify: [(2³)² × 2⁵] ÷ 2⁸ = ? 🌀", "options": {"A": "2²", "B": "2³", "C": "2⁵", "D": "2⁷"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "Find n: 9ⁿ = (27²)/(3³). 🧩", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "Simplify: (5p²q³)² × p⁴q = ? ✨", "options": {"A": "25p⁸q⁷", "B": "10p⁸q⁷", "C": "25p⁶q⁶", "D": "5p⁸q⁷"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "If a² = 16 and b³ = 27, find a² × b³. 🤝", "options": {"A": "432", "B": "43", "C": "432¹", "D": "69"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "Simplify: [(-3)⁴ × (-3)] ÷ (-3)² = ? ⚡", "options": {"A": "-27", "B": "27", "C": "-9", "D": "9"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Express 4⁵ × 16² as a power of 2. 🔄", "options": {"A": "2¹¹", "B": "2¹³", "C": "2¹⁵", "D": "2¹⁷"}, "correct_answer": "D"},
    {"id": 33, "difficulty": "medium", "question": "Simplify: (a⁰ + b⁰ + 5⁰)² = ? 🎲", "options": {"A": "1", "B": "3", "C": "9", "D": "25"}, "correct_answer": "C"},
    {"id": 34, "difficulty": "medium", "question": "Find x: (7²)ˣ = 7⁸ ÷ 7². ⚖️", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "Simplify: (2³ × 3²)² = ? 📦", "options": {"A": "2⁶ × 3⁴", "B": "2⁵ × 3⁴", "C": "6⁵", "D": "12⁶"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "If 2ⁿ × 4 = 2⁷, what is n? 🔢", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "C"},
    {"id": 37, "difficulty": "medium", "question": "Simplify: (x⁵y⁻²) × (x⁻³y⁴) (Assume x,y ≠ 0). 🍃", "options": {"A": "x²y²", "B": "x⁸y⁶", "C": "x²y⁻⁸", "D": "x⁻¹⁵y⁻⁸"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "What is (0.5)² expressed as a fraction? 🍕", "options": {"A": "1/8", "B": "1/2", "C": "1/4", "D": "1/16"}, "correct_answer": "C"},
    {"id": 39, "difficulty": "medium", "question": "Simplify: [(10²)³ ÷ 10⁴] × 10 = ? 💰", "options": {"A": "10³", "B": "10⁴", "C": "10⁵", "D": "10⁶"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "If (3ˣ)² = 81, find x. 🧭", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 41, "difficulty": "hard", "question": "Simplify: [ (2⁴ × 3³) / (6² × 2) ]² = ? 🏆", "options": {"A": "2⁴ × 3²", "B": "2⁶ × 3⁴", "C": "12⁴", "D": "6⁶"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "hard", "question": "Solve for x: 8ˣ⁺¹ = (32 × 2ˣ) / 4. ⚔️", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "C"},
    {"id": 43, "difficulty": "hard", "question": "If 2ᵃ = 3ᵇ = 6ᶜ, show that c = ab/(a+b). Find (1/a)+(1/b). 🤯", "options": {"A": "1/c", "B": "c", "C": "1", "D": "0"}, "correct_answer": "C"},
    {"id": 44, "difficulty": "hard", "question": "Simplify: {(aⁿ)ᵐ × (aᵐ)ⁿ} / (aᵐⁿ) = ? 🧬", "options": {"A": "1", "B": "aᵐⁿ", "C": "a²ᵐⁿ", "D": "0"}, "correct_answer": "B"},
    {"id": 45, "difficulty": "hard", "question": "Find the value of x if (√27)ˣ = (9ˣ⁺²)/(3ˣ). 🌳", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "D"},
    {"id": 46, "difficulty": "hard", "question": "Simplify: [{(2²)³ × 3⁵} / {2⁴ × 3³}]² = ? 🧱", "options": {"A": "2⁸ × 3⁴", "B": "2⁴ × 3⁸", "C": "12⁸", "D": "6¹²"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "hard", "question": "If 5²ˣ⁻¹ = 1/(125ˣ⁻³), find x. 🎭", "options": {"A": "1", "B": "2", "C": "10/7", "D": "5/3"}, "correct_answer": "C"},
    {"id": 48, "difficulty": "hard", "question": "Simplify: (256 × 16ⁿ⁺¹) / (4 × 8²ⁿ) 🌌", "options": {"A": "2⁸", "B": "2¹²", "C": "2⁴ⁿ⁺⁸", "D": "2²ⁿ⁺¹²"}, "correct_answer": "B"},
    {"id": 49, "difficulty": "hard", "question": "Prove step for simplification: (xᵃ⁻ᵇ)ᵃ⁺ᵇ × (xᵇ⁻ᶜ)ᵇ⁺ᶜ × (xᶜ⁻ᵃ)ᶜ⁺ᵃ = ? 🧩", "options": {"A": "x⁰", "B": "0", "C": "1", "D": "x²ᵃ²ᵇ²ᶜ"}, "correct_answer": "C"},
    {"id": 50, "difficulty": "hard", "question": "If 4ˣ = 8ʸ = 16ᶻ, find (1/x)+(1/y) in terms of z. 🔗", "options": {"A": "1/z", "B": "2/z", "C": "3/(2z)", "D": "5/(2z)"}, "correct_answer": "C"},
    {"id": 51, "difficulty": "hard", "question": "Simplify: [(81)^(3/4) × (16)^(1/4)] / [(36)^(1/2)] = ? 🧮", "options": {"A": "6", "B": "9", "C": "12", "D": "18"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "hard", "question": "Find x: 9 × 3ˣ = (27)² / (√3)ˣ. 🌀", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "hard", "question": "Simplify: { (5⁴ × 2⁶) / (10² × 4) }^(1/2) = ? 🪐", "options": {"A": "10", "B": "20", "C": "25", "D": "50"}, "correct_answer": "D"},
    {"id": 54, "difficulty": "hard", "question": "If a = 2¹⁰⁰, b = 3⁶⁰, c = 5⁵⁰, which is greatest? 👑", "options": {"A": "a", "B": "b", "C": "c", "D": "Cannot say"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "hard", "question": "Solve: (2ˣ × 5ˣ)² = 10¹² ÷ 10ˣ. ⏳", "options": {"A": "2", "B": "3", "C": "4", "D": "6"}, "correct_answer": "C"},
    {"id": 56, "difficulty": "hard", "question": "Simplify: (a¹/² × b³/⁴)⁸ ÷ (a² × b³) = ? 🍀", "options": {"A": "a²b³", "B": "a⁴b⁶", "C": "b³", "D": "1"}, "correct_answer": "C"},
    {"id": 57, "difficulty": "hard", "question": "If (0.04)⁻¹⋅⁵ = 5ⁿ, find n. ⚡", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 58, "difficulty": "hard", "question": "Find the value of: [{(0.6)²}³]⁻¹ × (0.6)⁴ ÷ (0.6)⁻². 🎢", "options": {"A": "0.6⁶", "B": "0.6¹⁰", "C": "1", "D": "0.6¹²"}, "correct_answer": "C"},
    {"id": 59, "difficulty": "hard", "question": "Simplify: (xᵃ / xᵇ)^(a+b) × (xᵇ / xᶜ)^(b+c) × (xᶜ / xᵃ)^(c+a) = ? ♾️", "options": {"A": "x⁰", "B": "0", "C": "1", "D": "x²⁽ᵃ²⁺ᵇ²⁺ᶜ²⁾"}, "correct_answer": "C"},
    {"id": 60, "difficulty": "hard", "question": "If 3^m = 5^n = (75)^p, prove that (1/m)+(2/n)=(3/p). Find 3p in terms of m & n. 🏹", "options": {"A": "m+n", "B": "m+2n", "C": "2m+n", "D": "mn/(m+n)"}, "correct_answer": "A"}
  ]
}