{
  "title": "Laws of Exponents for Real Numbers - Grade 9 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Simplify: 2³ × 2⁴", "options": {"A": "2⁷", "B": "2¹²", "C": "4⁷", "D": "8¹²"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "What is (5²)³?", "options": {"A": "5⁵", "B": "5⁶", "C": "5⁸", "D": "25³"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "Simplify: a⁵ ÷ a²", "options": {"A": "a³", "B": "a⁷", "C": "a¹⁰", "D": "a².⁵"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "What is 7⁰?", "options": {"A": "0", "B": "1", "C": "7", "D": "Undefined"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "Simplify: (3×4)²", "options": {"A": "3²×4", "B": "3×4²", "C": "3²×4²", "D": "7²"}, "correct_answer": "C"},
    {"id": 6, "difficulty": "easy", "question": "What is 10⁻²?", "options": {"A": "100", "B": "0.01", "C": "0.1", "D": "-100"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "Simplify: x⁴ × x⁻²", "options": {"A": "x²", "B": "x⁶", "C": "x⁻⁸", "D": "x⁻²"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "What is (2³)²?", "options": {"A": "2⁵", "B": "2⁶", "C": "4⁵", "D": "4⁶"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "Simplify: (5² × 5³) ÷ 5⁴", "options": {"A": "5", "B": "5²", "C": "5⁹", "D": "5¹"}, "correct_answer": "D"},
    {"id": 10, "difficulty": "easy", "question": "What is (a³)⁴?", "options": {"A": "a⁷", "B": "a¹²", "C": "a⁸¹", "D": "a⁶⁴"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "Simplify: 6⁵ ÷ 6³", "options": {"A": "6²", "B": "6⁸", "C": "6¹⁵", "D": "36²"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "What is 100⁰?", "options": {"A": "0", "B": "1", "C": "100", "D": "10"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "Simplify: (2x)³", "options": {"A": "2x³", "B": "8x³", "C": "6x³", "D": "2³x"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "What is 5⁻¹?", "options": {"A": "-5", "B": "0.2", "C": "0.5", "D": "1/5"}, "correct_answer": "D"},
    {"id": 15, "difficulty": "easy", "question": "Simplify: y⁷ ÷ y⁷", "options": {"A": "y⁰", "B": "1", "C": "0", "D": "y¹⁴"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "What is (4²)⁰?", "options": {"A": "0", "B": "1", "C": "4", "D": "16"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "Simplify: 3² × 3³", "options": {"A": "3⁵", "B": "3⁶", "C": "9⁵", "D": "27²"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "What is (1/2)⁻¹?", "options": {"A": "2", "B": "0.5", "C": "-0.5", "D": "-2"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "Simplify: a⁰ × b⁰", "options": {"A": "0", "B": "1", "C": "a+b", "D": "ab"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "What is 2⁴ ÷ 2²?", "options": {"A": "2²", "B": "2⁶", "C": "4²", "D": "1²"}, "correct_answer": "A"},

    {"id": 21, "difficulty": "medium", "question": "Simplify: (2³ × 3²)²", "options": {"A": "2⁶ × 3⁴", "B": "2⁵ × 3⁴", "C": "2⁹ × 3⁴", "D": "4⁶ × 9⁴"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "What is (x²y³)⁴?", "options": {"A": "x⁶y⁷", "B": "x⁸y¹²", "C": "x⁶y¹²", "D": "x⁸y⁷"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "Simplify: (a⁻³ × b²)⁻²", "options": {"A": "a⁶b⁻⁴", "B": "a⁻⁶b⁴", "C": "a⁶b⁴", "D": "a⁻¹²b⁻⁴"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "Find x if 2ˣ = 16", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 25, "difficulty": "medium", "question": "Simplify: (27)^(2/3)", "options": {"A": "3", "B": "6", "C": "9", "D": "18"}, "correct_answer": "C"},
    {"id": 26, "difficulty": "medium", "question": "What is 125^(-1/3)?", "options": {"A": "5", "B": "1/5", "C": "25", "D": "1/25"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "Simplify: √(x⁶)", "options": {"A": "x³", "B": "x⁴", "C": "x⁶", "D": "x¹²"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "If 3ⁿ = 81, find n", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 29, "difficulty": "medium", "question": "Simplify: (16)^(3/4)", "options": {"A": "4", "B": "8", "C": "12", "D": "16"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "What is (8/27)^(-2/3)?", "options": {"A": "4/9", "B": "9/4", "C": "2/3", "D": "3/2"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "Simplify: (x⁻²y³)/(x⁴y⁻¹)", "options": {"A": "x⁻⁶y⁴", "B": "x²y²", "C": "x⁻²y⁴", "D": "y⁴/x⁶"}, "correct_answer": "D"},
    {"id": 32, "difficulty": "medium", "question": "Find x if 5ˣ⁻¹ = 25", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "C"},
    {"id": 33, "difficulty": "medium", "question": "Simplify: (9)^(3/2)", "options": {"A": "3", "B": "9", "C": "18", "D": "27"}, "correct_answer": "D"},
    {"id": 34, "difficulty": "medium", "question": "What is 32^(2/5)?", "options": {"A": "2", "B": "4", "C": "8", "D": "16"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "Simplify: (a²b⁻³)² × (a⁻¹b²)³", "options": {"A": "a b⁰", "B": "a⁷b⁻¹²", "C": "a b⁻⁵", "D": "a⁴b⁻¹⁸"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "If 2^(x+1) = 8, find x", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "Simplify: (64)^(-2/3)", "options": {"A": "1/4", "B": "1/8", "C": "1/16", "D": "1/32"}, "correct_answer": "C"},
    {"id": 38, "difficulty": "medium", "question": "What is (x¹/² × x³/⁴) ÷ x¹/⁴?", "options": {"A": "x", "B": "x¹/²", "C": "x³/⁴", "D": "x⁵/⁴"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Simplify: ∛(x⁹)", "options": {"A": "x³", "B": "x⁶", "C": "x⁹", "D": "x²⁷"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "If 10^x = 1000, find x", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 41, "difficulty": "medium", "question": "Simplify: (25)^(3/2)", "options": {"A": "5", "B": "25", "C": "125", "D": "625"}, "correct_answer": "C"},
    {"id": 42, "difficulty": "medium", "question": "What is (1/16)^(-1/4)?", "options": {"A": "2", "B": "4", "C": "8", "D": "16"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "Simplify: (x²/³ × x⁴/³) ÷ x¹/³", "options": {"A": "x¹/³", "B": "x²/³", "C": "x⁵/³", "D": "x⁷/³"}, "correct_answer": "C"},
    {"id": 44, "difficulty": "medium", "question": "Find x if 4^(2x-1) = 64", "options": {"A": "1", "B": "1.5", "C": "2", "D": "2.5"}, "correct_answer": "C"},
    {"id": 45, "difficulty": "medium", "question": "Simplify: (81)^(3/4)", "options": {"A": "9", "B": "18", "C": "27", "D": "81"}, "correct_answer": "C"},
    {"id": 46, "difficulty": "medium", "question": "What is (8)^(-4/3)?", "options": {"A": "1/4", "B": "1/8", "C": "1/16", "D": "1/32"}, "correct_answer": "C"},
    {"id": 47, "difficulty": "medium", "question": "Simplify: √(a⁴b⁶)", "options": {"A": "a²b³", "B": "a²b⁴", "C": "a⁴b³", "D": "a⁸b¹²"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "If 3^(2x) = 27, find x", "options": {"A": "1", "B": "1.5", "C": "2", "D": "2.5"}, "correct_answer": "B"},
    {"id": 49, "difficulty": "medium", "question": "Simplify: (36)^(1.5)", "options": {"A": "6", "B": "36", "C": "108", "D": "216"}, "correct_answer": "D"},
    {"id": 50, "difficulty": "medium", "question": "What is (27/8)^(2/3)?", "options": {"A": "3/2", "B": "9/4", "C": "4/9", "D": "2/3"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "medium", "question": "Simplify: (x⁻³y²)⁻² × (x²y⁻¹)³", "options": {"A": "x¹⁰y⁻⁷", "B": "x²y", "C": "x⁻¹⁰y⁷", "D": "y/x"}, "correct_answer": "B"},
    {"id": 52, "difficulty": "medium", "question": "Find x if 5^(x+2) = 125", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "medium", "question": "Simplify: (1000)^(2/3)", "options": {"A": "10", "B": "100", "C": "1000", "D": "10000"}, "correct_answer": "B"},
    {"id": 54, "difficulty": "medium", "question": "What is (1/9)^(-3/2)?", "options": {"A": "3", "B": "9", "C": "27", "D": "81"}, "correct_answer": "C"},
    {"id": 55, "difficulty": "medium", "question": "Simplify: ∛(x⁶y⁹)", "options": {"A": "x²y³", "B": "x³y⁶", "C": "x⁶y⁹", "D": "x¹⁸y²⁷"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "medium", "question": "If 2^(3x-1) = 32, find x", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 57, "difficulty": "medium", "question": "Simplify: (49)^(3/2)", "options": {"A": "7", "B": "49", "C": "343", "D": "2401"}, "correct_answer": "C"},
    {"id": 58, "difficulty": "medium", "question": "What is (32)^(-3/5)?", "options": {"A": "1/2", "B": "1/4", "C": "1/8", "D": "1/16"}, "correct_answer": "C"},
    {"id": 59, "difficulty": "medium", "question": "Simplify: (x¹/⁴ × x³/⁴)²", "options": {"A": "x", "B": "x²", "C": "x⁴", "D": "x⁸"}, "correct_answer": "B"},
    {"id": 60, "difficulty": "medium", "question": "If 4^x = 1/64, find x", "options": {"A": "-2", "B": "-3", "C": "2", "D": "3"}, "correct_answer": "B"},
    {"id": 61, "difficulty": "medium", "question": "Simplify: (144)^(0.5)", "options": {"A": "12", "B": "14.4", "C": "72", "D": "144"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "What is (1/125)^(-2/3)?", "options": {"A": "5", "B": "25", "C": "125", "D": "625"}, "correct_answer": "B"},
    {"id": 63, "difficulty": "medium", "question": "Simplify: √(x⁸y¹²)", "options": {"A": "x⁴y⁶", "B": "x⁸y¹²", "C": "x¹⁶y²⁴", "D": "x⁴y¹²"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "medium", "question": "If 9^(x-1) = 27, find x", "options": {"A": "1.5", "B": "2", "C": "2.5", "D": "3"}, "correct_answer": "C"},
    {"id": 65, "difficulty": "medium", "question": "Simplify: (216)^(2/3)", "options": {"A": "6", "B": "12", "C": "36", "D": "216"}, "correct_answer": "C"},
    {"id": 66, "difficulty": "medium", "question": "What is (16/81)^(-3/4)?", "options": {"A": "8/27", "B": "27/8", "C": "4/9", "D": "9/4"}, "correct_answer": "B"},
    {"id": 67, "difficulty": "medium", "question": "Simplify: (x⁻¹/² × x³/²) ÷ x¹/²", "options": {"A": "x⁻¹/²", "B": "x⁰", "C": "x¹/²", "D": "x³/²"}, "correct_answer": "B"},
    {"id": 68, "difficulty": "medium", "question": "If 8^x = 32, find x", "options": {"A": "1", "B": "1.2", "C": "1.5", "D": "1.667"}, "correct_answer": "D"},
    {"id": 69, "difficulty": "medium", "question": "Simplify: (100)^(1.5)", "options": {"A": "10", "B": "100", "C": "1000", "D": "10000"}, "correct_answer": "C"},
    {"id": 70, "difficulty": "medium", "question": "What is (1/64)^(-2/3)?", "options": {"A": "4", "B": "8", "C": "16", "D": "32"}, "correct_answer": "C"},
    {"id": 71, "difficulty": "medium", "question": "Simplify: ∛(8x⁶y¹²)", "options": {"A": "2x²y⁴", "B": "2x³y⁶", "C": "4x²y⁴", "D": "8x²y⁴"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "medium", "question": "If 25^(x+1) = 125, find x", "options": {"A": "-0.5", "B": "0", "C": "0.5", "D": "1"}, "correct_answer": "C"},
    {"id": 73, "difficulty": "medium", "question": "Simplify: (343)^(2/3)", "options": {"A": "7", "B": "14", "C": "49", "D": "343"}, "correct_answer": "C"},
    {"id": 74, "difficulty": "medium", "question": "What is (27/64)^(-2/3)?", "options": {"A": "4/9", "B": "9/4", "C": "16/81", "D": "81/16"}, "correct_answer": "B"},
    {"id": 75, "difficulty": "medium", "question": "Simplify: (x²/³ × x⁴/³)³", "options": {"A": "x²", "B": "x⁶", "C": "x⁸", "D": "x¹²"}, "correct_answer": "B"},
    {"id": 76, "difficulty": "medium", "question": "If 16^(2x) = 64, find x", "options": {"A": "0.5", "B": "0.75", "C": "1", "D": "1.5"}, "correct_answer": "B"},
    {"id": 77, "difficulty": "medium", "question": "Simplify: (625)^(0.75)", "options": {"A": "25", "B": "125", "C": "625", "D": "3125"}, "correct_answer": "B"},
    {"id": 78, "difficulty": "medium", "question": "What is (1/32)^(-3/5)?", "options": {"A": "2", "B": "4", "C": "8", "D": "16"}, "correct_answer": "C"},
    {"id": 79, "difficulty": "medium", "question": "Simplify: √(16x⁸)", "options": {"A": "4x⁴", "B": "4x⁸", "C": "8x⁴", "D": "16x⁴"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "If 10^(2x) = 0.001, find x", "options": {"A": "-1.5", "B": "-1", "C": "-0.5", "D": "0"}, "correct_answer": "A"},

    {"id": 81, "difficulty": "hard", "question": "Simplify: [{(2³)²}⁰]⁵", "options": {"A": "0", "B": "1", "C": "2³⁰", "D": "2⁰"}, "correct_answer": "B"},
    {"id": 82, "difficulty": "hard", "question": "If 2^x = 3^y = 6^z, express z in terms of x and y", "options": {"A": "z = xy/(x+y)", "B": "z = (x+y)/xy", "C": "z = xy/(x-y)", "D": "z = x+y"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "Simplify: (√5)^(log₅4)", "options": {"A": "2", "B": "√2", "C": "4", "D": "5"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "If a^m × a^n = a^(m+n), what is a^m ÷ a^n?", "options": {"A": "a^(m-n)", "B": "a^(mn)", "C": "a^(m/n)", "D": "a^(n-m)"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "Simplify: [{(3²)³}²] ÷ 3¹⁰", "options": {"A": "3²", "B": "3⁴", "C": "3⁸", "D": "3¹²"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "If 4^(x+1) = 8^(x-1), find x", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "C"},
    {"id": 87, "difficulty": "hard", "question": "Simplify: (x^a-b)^(a+b) × (x^b-c)^(b+c) × (x^c-a)^(c+a)", "options": {"A": "0", "B": "1", "C": "x", "D": "x^(a²+b²+c²)"}, "correct_answer": "B"},
    {"id": 88, "difficulty": "hard", "question": "If 3^(2x+1) = 9^(x-2), find x", "options": {"A": "-3", "B": "-4", "C": "-5", "D": "-6"}, "correct_answer": "C"},
    {"id": 89, "difficulty": "hard", "question": "Simplify: [(2^n × 4^n)/(8^(n/3))]^(1/n)", "options": {"A": "2", "B": "4", "C": "8", "D": "16"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "If a^x = b, b^y = c, c^z = a, find xyz", "options": {"A": "0", "B": "1", "C": "abc", "D": "a+b+c"}, "correct_answer": "B"},
    {"id": 91, "difficulty": "hard", "question": "Simplify: (256)^(0.16) × (256)^(0.09)", "options": {"A": "4", "B": "16", "C": "64", "D": "256"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "If 2^(x) = 4^(y) = 8^(z) and xyz = 288, find x", "options": {"A": "12", "B": "24", "C": "36", "D": "48"}, "correct_answer": "B"},
    {"id": 93, "difficulty": "hard", "question": "Simplify: [{(5²)³}⁴] ÷ 5²³", "options": {"A": "5", "B": "5²", "C": "5³", "D": "5⁴"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "If (√3)^x = 3^(x/2), what is (∛9)^x?", "options": {"A": "3^(x/3)", "B": "3^(2x/3)", "C": "3^(3x/2)", "D": "3^x"}, "correct_answer": "B"},
    {"id": 95, "difficulty": "hard", "question": "Simplify: (a^m)^n × (a^n)^m ÷ (a^(mn))", "options": {"A": "a^(mn)", "B": "a^(2mn)", "C": "1", "D": "a^(m+n)"}, "correct_answer": "C"},
    {"id": 96, "difficulty": "hard", "question": "If 27^x = 9, find 3^(2x+1)", "options": {"A": "3", "B": "6", "C": "9", "D": "27"}, "correct_answer": "B"},
    {"id": 97, "difficulty": "hard", "question": "Simplify: [(x^a/x^b)^(a+b)] × [(x^b/x^c)^(b+c)] × [(x^c/x^a)^(c+a)]", "options": {"A": "0", "B": "1", "C": "x", "D": "x^(a²+b²+c²)"}, "correct_answer": "B"},
    {"id": 98, "difficulty": "hard", "question": "If 5^(2x) × 5^(3) = 5^(11), find x", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 99, "difficulty": "hard", "question": "Simplify: (4^(2.5) × 8^(1.5)) / (16^(2))", "options": {"A": "0.5", "B": "1", "C": "2", "D": "4"}, "correct_answer": "B"},
    {"id": 100, "difficulty": "hard", "question": "If 2^(x+y) = 16 and 2^(x-y) = 4, find x and y", "options": {"A": "x=3, y=1", "B": "x=4, y=2", "C": "x=3.5, y=0.5", "D": "x=2.5, y=1.5"}, "correct_answer": "A"}
  ]
}