{
  "title": "Laws of Exponents - Grade 8 ICSE",
  "total_questions": 60,
  "questions": [
    {
      "id": 1,
      "difficulty": "easy",
      "question": "What is 2³ × 2²? ✨",
      "options": { "A": "2⁵", "B": "2⁶", "C": "4⁵", "D": "4⁶" },
      "correct_answer": "A"
    },
    {
      "id": 2,
      "difficulty": "easy",
      "question": "Simplify: 5⁴ ÷ 5² 🧮",
      "options": { "A": "5²", "B": "5⁶", "C": "5⁸", "D": "5⁻²" },
      "correct_answer": "A"
    },
    {
      "id": 3,
      "difficulty": "easy",
      "question": "What is (3²)³? 📚",
      "options": { "A": "3⁵", "B": "3⁶", "C": "9⁵", "D": "9⁶" },
      "correct_answer": "B"
    },
    {
      "id": 4,
      "difficulty": "easy",
      "question": "Simplify: 7⁵ × 7⁰ ⚡",
      "options": { "A": "7⁵", "B": "7⁶", "C": "0", "D": "1" },
      "correct_answer": "A"
    },
    {
      "id": 5,
      "difficulty": "easy",
      "question": "What is 4⁻² as a positive exponent? 🔄",
      "options": { "A": "1/4²", "B": "4²", "C": "-4²", "D": "1/4⁻²" },
      "correct_answer": "A"
    },
    {
      "id": 6,
      "difficulty": "easy",
      "question": "Simplify: 10⁶ ÷ 10⁴ 🔢",
      "options": { "A": "10²", "B": "10¹⁰", "C": "10²⁴", "D": "10⁻²" },
      "correct_answer": "A"
    },
    {
      "id": 7,
      "difficulty": "easy",
      "question": "What is (2³)²? 🎯",
      "options": { "A": "2⁵", "B": "2⁶", "C": "4⁵", "D": "4⁶" },
      "correct_answer": "B"
    },
    {
      "id": 8,
      "difficulty": "easy",
      "question": "Simplify: 6⁷ ÷ 6⁵ ➗",
      "options": { "A": "6²", "B": "6¹²", "C": "6³⁵", "D": "6⁻²" },
      "correct_answer": "A"
    },
    {
      "id": 9,
      "difficulty": "easy",
      "question": "What is 9⁰? ❓",
      "options": { "A": "0", "B": "1", "C": "9", "D": "Undefined" },
      "correct_answer": "B"
    },
    {
      "id": 10,
      "difficulty": "easy",
      "question": "Simplify: a³ × a⁴ (where a is any number) 📝",
      "options": { "A": "a⁷", "B": "a¹²", "C": "a", "D": "a⁻¹" },
      "correct_answer": "A"
    },
    {
      "id": 11,
      "difficulty": "easy",
      "question": "What is 5 × 5³? ✖️",
      "options": { "A": "5³", "B": "5⁴", "C": "25³", "D": "5⁵" },
      "correct_answer": "B"
    },
    {
      "id": 12,
      "difficulty": "easy",
      "question": "Simplify: (4²)² 📐",
      "options": { "A": "4⁴", "B": "4⁶", "C": "16²", "D": "8⁴" },
      "correct_answer": "A"
    },
    {
      "id": 13,
      "difficulty": "easy",
      "question": "What is 8¹? 🎲",
      "options": { "A": "0", "B": "1", "C": "8", "D": "16" },
      "correct_answer": "C"
    },
    {
      "id": 14,
      "difficulty": "easy",
      "question": "Simplify: x⁵ ÷ x² (x ≠ 0) ➗",
      "options": { "A": "x³", "B": "x⁷", "C": "x¹⁰", "D": "x².⁵" },
      "correct_answer": "A"
    },
    {
      "id": 15,
      "difficulty": "easy",
      "question": "What is (5³)⁰? ⭐",
      "options": { "A": "0", "B": "1", "C": "5³", "D": "5⁰" },
      "correct_answer": "B"
    },
    {
      "id": 16,
      "difficulty": "easy",
      "question": "Simplify: 3⁴ × 3² 🔢",
      "options": { "A": "3⁶", "B": "3⁸", "C": "9⁶", "D": "9⁸" },
      "correct_answer": "A"
    },
    {
      "id": 17,
      "difficulty": "easy",
      "question": "What is 7⁻¹? 🔄",
      "options": { "A": "-7", "B": "1/7", "C": "7", "D": "0" },
      "correct_answer": "B"
    },
    {
      "id": 18,
      "difficulty": "easy",
      "question": "Simplify: (2 × 3)² 🧩",
      "options": {
        "A": "2² × 3²",
        "B": "2² + 3²",
        "C": "5²",
        "D": "6²"
      },
      "correct_answer": "D"
    },
    {
      "id": 19,
      "difficulty": "easy",
      "question": "What is 10⁵ ÷ 10⁵? ⚖️",
      "options": { "A": "0", "B": "1", "C": "10", "D": "10¹⁰" },
      "correct_answer": "B"
    },
    {
      "id": 20,
      "difficulty": "easy",
      "question": "Simplify: y⁶ ÷ y⁶ (y ≠ 0) ✅",
      "options": { "A": "0", "B": "1", "C": "y", "D": "y¹²" },
      "correct_answer": "B"
    },
    {
      "id": 21,
      "difficulty": "medium",
      "question": "Simplify: (2³ × 2⁴) ÷ 2⁵ 🧠",
      "options": {
        "A": "2²",
        "B": "2⁷",
        "C": "2¹²",
        "D": "4²"
      },
      "correct_answer": "A"
    },
    {
      "id": 22,
      "difficulty": "medium",
      "question": "What is (5² × 5³) ÷ 5⁴? 📊",
      "options": {
        "A": "5",
        "B": "5²",
        "C": "5³",
        "D": "5⁰"
      },
      "correct_answer": "A"
    },
    {
      "id": 23,
      "difficulty": "medium",
      "question": "Simplify: (3⁻² × 3⁵) ÷ 3² 🔄",
      "options": {
        "A": "3",
        "B": "3²",
        "C": "3⁻¹",
        "D": "3⁰"
      },
      "correct_answer": "A"
    },
    {
      "id": 24,
      "difficulty": "medium",
      "question": "What is (4³)² ÷ 4⁵? ➗",
      "options": {
        "A": "4",
        "B": "4²",
        "C": "4³",
        "D": "4⁶"
      },
      "correct_answer": "A"
    },
    {
      "id": 25,
      "difficulty": "medium",
      "question": "Simplify: (a⁵ × a⁻³) ÷ a² (a ≠ 0) 📝",
      "options": {
        "A": "a⁰",
        "B": "a²",
        "C": "a⁴",
        "D": "a⁻⁴"
      },
      "correct_answer": "A"
    },
    {
      "id": 26,
      "difficulty": "medium",
      "question": "What is (7⁴ × 7⁻²) ÷ 7³? 🧮",
      "options": {
        "A": "7⁻¹",
        "B": "7",
        "C": "7²",
        "D": "7³"
      },
      "correct_answer": "A"
    },
    {
      "id": 27,
      "difficulty": "medium",
      "question": "Simplify: (2²)³ × 2⁻⁴ ⚡",
      "options": {
        "A": "2²",
        "B": "2⁶",
        "C": "2⁻²",
        "D": "2¹⁰"
      },
      "correct_answer": "A"
    },
    {
      "id": 28,
      "difficulty": "medium",
      "question": "What is (10³ ÷ 10⁵) × 10⁴? 🔢",
      "options": {
        "A": "10²",
        "B": "10⁻²",
        "C": "10¹²",
        "D": "10"
      },
      "correct_answer": "A"
    },
    {
      "id": 29,
      "difficulty": "medium",
      "question": "Simplify: (5⁻¹ × 5⁴) ÷ 5² 🎯",
      "options": {
        "A": "5",
        "B": "5²",
        "C": "5⁻¹",
        "D": "5⁰"
      },
      "correct_answer": "A"
    },
    {
      "id": 30,
      "difficulty": "medium",
      "question": "What is (x⁶ ÷ x²) × x⁻³? (x ≠ 0) 📚",
      "options": {
        "A": "x",
        "B": "x²",
        "C": "x⁻¹",
        "D": "x⁰"
      },
      "correct_answer": "A"
    },
    {
      "id": 31,
      "difficulty": "medium",
      "question": "Simplify: (3² × 3⁻⁵) × 3⁶ 🔄",
      "options": {
        "A": "3³",
        "B": "3²",
        "C": "3⁰",
        "D": "3⁻⁷"
      },
      "correct_answer": "A"
    },
    {
      "id": 32,
      "difficulty": "medium",
      "question": "What is (2⁴ ÷ 2)²? ➗",
      "options": {
        "A": "2⁶",
        "B": "2⁸",
        "C": "2⁷",
        "D": "2⁵"
      },
      "correct_answer": "A"
    },
    {
      "id": 33,
      "difficulty": "medium",
      "question": "Simplify: (a⁻² × a⁵) ÷ a⁻¹ (a ≠ 0) ✨",
      "options": {
        "A": "a²",
        "B": "a⁴",
        "C": "a⁶",
        "D": "a⁸"
      },
      "correct_answer": "B"
    },
    {
      "id": 34,
      "difficulty": "medium",
      "question": "What is (6³ × 6⁻¹) ÷ 6²? 🧩",
      "options": {
        "A": "6⁰",
        "B": "6²",
        "C": "6⁻²",
        "D": "6⁴"
      },
      "correct_answer": "A"
    },
    {
      "id": 35,
      "difficulty": "medium",
      "question": "Simplify: (4⁻² × 4⁵) ÷ 4³ 📐",
      "options": {
        "A": "4⁰",
        "B": "4²",
        "C": "4⁻²",
        "D": "4⁴"
      },
      "correct_answer": "A"
    },
    {
      "id": 36,
      "difficulty": "medium",
      "question": "What is (10²)³ ÷ 10⁵? ⚖️",
      "options": {
        "A": "10",
        "B": "10²",
        "C": "10⁻¹",
        "D": "10⁰"
      },
      "correct_answer": "A"
    },
    {
      "id": 37,
      "difficulty": "medium",
      "question": "Simplify: (m⁴ × m⁻²) × m³ (m ≠ 0) 📝",
      "options": {
        "A": "m⁵",
        "B": "m³",
        "C": "m⁰",
        "D": "m⁻⁵"
      },
      "correct_answer": "A"
    },
    {
      "id": 38,
      "difficulty": "medium",
      "question": "What is (9² ÷ 9⁻¹) × 9⁻²? 🔢",
      "options": {
        "A": "9³",
        "B": "9",
        "C": "9⁻¹",
        "D": "9⁰"
      },
      "correct_answer": "B"
    },
    {
      "id": 39,
      "difficulty": "medium",
      "question": "Simplify: (5² × 5⁻³) ÷ 5⁻¹ 🧮",
      "options": {
        "A": "5⁰",
        "B": "5⁻²",
        "C": "5⁻⁴",
        "D": "5²"
      },
      "correct_answer": "A"
    },
    {
      "id": 40,
      "difficulty": "medium",
      "question": "What is (2⁵ ÷ 2³) × 2⁻¹? ➖",
      "options": {
        "A": "2",
        "B": "2²",
        "C": "2⁻¹",
        "D": "2⁰"
      },
      "correct_answer": "A"
    },
    {
      "id": 41,
      "difficulty": "hard",
      "question": "Simplify: [(3²)³ × 3⁻⁴] ÷ 3³ 🧠",
      "options": {
        "A": "3⁻¹",
        "B": "3",
        "C": "3²",
        "D": "3⁰"
      },
      "correct_answer": "A"
    },
    {
      "id": 42,
      "difficulty": "hard",
      "question": "What is (2⁴ × 2⁻⁶) ÷ (2² × 2⁻³)? 📊",
      "options": {
        "A": "2⁻⁵",
        "B": "2⁻³",
        "C": "2⁻¹",
        "D": "2⁰"
      },
      "correct_answer": "B"
    },
    {
      "id": 43,
      "difficulty": "hard",
      "question": "Simplify: (a²b³)² ÷ (a³b)³ (a,b ≠ 0) 🔄",
      "options": {
        "A": "a⁻⁵b³",
        "B": "a⁵b⁻³",
        "C": "a⁻⁵b⁻³",
        "D": "a⁵b³"
      },
      "correct_answer": "A"
    },
    {
      "id": 44,
      "difficulty": "hard",
      "question": "What is [(5³)² ÷ 5⁴] × 5⁻²? ➗",
      "options": {
        "A": "5⁰",
        "B": "5²",
        "C": "5⁻²",
        "D": "5⁴"
      },
      "correct_answer": "A"
    },
    {
      "id": 45,
      "difficulty": "hard",
      "question": "Simplify: (x⁴y⁻²)³ ÷ (x²y)⁴ (x,y ≠ 0) 📝",
      "options": {
        "A": "x⁶y⁻¹⁰",
        "B": "x⁻⁶y¹⁰",
        "C": "x⁰y⁰",
        "D": "x¹²y⁻⁶"
      },
      "correct_answer": "A"
    },
    {
      "id": 46,
      "difficulty": "hard",
      "question": "What is (10⁻³ × 10⁵) ÷ (10² × 10⁻⁴)? ⚡",
      "options": {
        "A": "10⁴",
        "B": "10²",
        "C": "10⁰",
        "D": "10⁻⁴"
      },
      "correct_answer": "A"
    },
    {
      "id": 47,
      "difficulty": "hard",
      "question": "Simplify: [(2⁻²)³ × 2⁵] ÷ 2⁻³ 🔢",
      "options": {
        "A": "2²",
        "B": "2⁸",
        "C": "2⁻⁸",
        "D": "2⁰"
      },
      "correct_answer": "B"
    },
    {
      "id": 48,
      "difficulty": "hard",
      "question": "What is (m³n⁻²)² ÷ (m⁻¹n³)³? (m,n ≠ 0) 🧩",
      "options": {
        "A": "m⁹n⁻¹³",
        "B": "m⁻⁹n¹³",
        "C": "m³n⁻⁵",
        "D": "m⁶n⁻⁴"
      },
      "correct_answer": "A"
    },
    {
      "id": 49,
      "difficulty": "hard",
      "question": "Simplify: (3² × 3⁻⁴) ÷ (3³ × 3⁻⁵) 📚",
      "options": {
        "A": "3⁰",
        "B": "3²",
        "C": "3⁻²",
        "D": "3⁴"
      },
      "correct_answer": "A"
    },
    {
      "id": 50,
      "difficulty": "hard",
      "question": "What is [(4³)⁻¹ × 4⁵] ÷ 4⁻²? 🎯",
      "options": {
        "A": "4⁴",
        "B": "4⁶",
        "C": "4⁻⁴",
        "D": "4⁰"
      },
      "correct_answer": "A"
    },
    {
      "id": 51,
      "difficulty": "hard",
      "question": "Simplify: (p⁻²q³)⁻¹ ÷ (p³q⁻²)² (p,q ≠ 0) 🔄",
      "options": {
        "A": "p⁻⁴q⁻¹",
        "B": "p⁴q",
        "C": "p⁻¹q⁴",
        "D": "p⁸q⁻⁷"
      },
      "correct_answer": "A"
    },
    {
      "id": 52,
      "difficulty": "hard",
      "question": "What is (6⁻² × 6⁴) ÷ (6³ × 6⁻⁵)? ➗",
      "options": {
        "A": "6⁴",
        "B": "6²",
        "C": "6⁰",
        "D": "6⁻²"
      },
      "correct_answer": "A"
    },
    {
      "id": 53,
      "difficulty": "hard",
      "question": "Simplify: (a²b⁻³c)³ ÷ (a⁻¹b²c⁻²)² (a,b,c ≠ 0) 📐",
      "options": {
        "A": "a⁸b⁻¹³c⁷",
        "B": "a⁴b⁻⁷c⁵",
        "C": "a⁶b⁻⁵c⁻¹",
        "D": "a⁰b⁰c⁰"
      },
      "correct_answer": "A"
    },
    {
      "id": 54,
      "difficulty": "hard",
      "question": "What is [(2⁻³)² × 2⁵] ÷ 2⁻⁴? ⚖️",
      "options": {
        "A": "2³",
        "B": "2⁵",
        "C": "2⁷",
        "D": "2⁹"
      },
      "correct_answer": "A"
    },
    {
      "id": 55,
      "difficulty": "hard",
      "question": "Simplify: (x³y⁻²z)² ÷ (x⁻²y³z⁻¹)³ (x,y,z ≠ 0) ✨",
      "options": {
        "A": "x¹²y⁻¹³z⁵",
        "B": "x⁶y⁻⁵z⁻¹",
        "C": "x⁰y⁰z⁰",
        "D": "x⁹y⁻⁴z⁻²"
      },
      "correct_answer": "A"
    },
    {
      "id": 56,
      "difficulty": "hard",
      "question": "What is (5⁴ × 5⁻⁶) ÷ (5² × 5⁻³)? 🔢",
      "options": {
        "A": "5⁻¹",
        "B": "5⁻³",
        "C": "5⁻⁵",
        "D": "5⁰"
      },
      "correct_answer": "A"
    },
    {
      "id": 57,
      "difficulty": "hard",
      "question": "Simplify: [(3⁻²)³ × 3⁴] ÷ 3⁻⁵ 🧮",
      "options": {
        "A": "3³",
        "B": "3⁵",
        "C": "3⁷",
        "D": "3⁹"
      },
      "correct_answer": "A"
    },
    {
      "id": 58,
      "difficulty": "hard",
      "question": "What is (m⁻²n³)² ÷ (m³n⁻²)⁻¹? (m,n ≠ 0) 📝",
      "options": {
        "A": "m⁻⁷n⁸",
        "B": "m⁻¹n⁴",
        "C": "m⁷n⁻⁸",
        "D": "m⁰n⁰"
      },
      "correct_answer": "A"
    },
    {
      "id": 59,
      "difficulty": "hard",
      "question": "Simplify: (2³ × 2⁻⁵) ÷ (2⁻² × 2⁴) ➖",
      "options": {
        "A": "2⁻⁴",
        "B": "2⁻²",
        "C": "2²",
        "D": "2⁴"
      },
      "correct_answer": "A"
    },
    {
      "id": 60,
      "difficulty": "hard",
      "question": "What is [(4⁻²)³ × 4⁵] ÷ 4⁻³? 🎲",
      "options": {
        "A": "4²",
        "B": "4⁴",
        "C": "4⁶",
        "D": "4⁸"
      },
      "correct_answer": "A"
    }
  ]
}