{
  "operaciones-numeros-reales": [
    {
      "id": "onr-001",
      "topic": "potencias-exponentes",
      "question": "Simplifica: $2^3 \\cdot 2^4$",
      "type": "multiple-choice",
      "shuffle": true,
      "options": [
        "$2^7 = 128$ (sumar exponentes)",
        "$2^{12}$ (multiplicar exponentes)",
        "$4^7$",
        "$8 \\cdot 16 = 128$ sin simplificar"
      ],
      "correct": 0,
      "difficulty": "facil",
      "hints": [
        "Cuando multiplicas potencias con la misma base, SUMAS los exponentes",
        "$a^m \\cdot a^n = a^{m+n}$",
        "$2^3 \\cdot 2^4 = 2^{3+4} = 2^7$"
      ],
      "stepByStep": [
        "📚 **Propiedades de Exponentes**",
        "",
        "**Propiedad:** $a^m \\cdot a^n = a^{m+n}$",
        "",
        "**Aplicación:**",
        "$$2^3 \\cdot 2^4 = 2^{3+4} = 2^7$$",
        "",
        "**Cálculo:**",
        "$$2^7 = 2 \\times 2 \\times 2 \\times 2 \\times 2 \\times 2 \\times 2 = 128$$",
        "",
        "**Verificación:**",
        "* $2^3 = 8$",
        "* $2^4 = 16$",
        "* $8 \\times 16 = 128$ ✓",
        "",
        "✅ **$2^7 = 128$**"
      ],
      "explanation": "Al multiplicar potencias de igual base, se suman los exponentes: 2³·2⁴ = 2⁷ = 128"
    },
    {
      "id": "onr-002",
      "topic": "raices-radicales",
      "question": "Simplifica: $\\sqrt{50}$",
      "type": "multiple-choice",
      "shuffle": true,
      "options": [
        "$5\\sqrt{2}$",
        "$25\\sqrt{2}$",
        "$2\\sqrt{5}$",
        "$\\sqrt{50}$ (no se puede simplificar)"
      ],
      "correct": 0,
      "difficulty": "medio",
      "hints": [
        "Busca factores que sean cuadrados perfectos",
        "50 = 25 × 2",
        "$\\sqrt{25 \\times 2} = \\sqrt{25} \\times \\sqrt{2} = 5\\sqrt{2}$"
      ],
      "stepByStep": [
        "🔍 **Simplificar Radicales**",
        "",
        "**Método:** Factorizar en cuadrados perfectos",
        "",
        "**Paso 1:** Descomponer 50",
        "$$50 = 25 \\times 2 = 5^2 \\times 2$$",
        "",
        "**Paso 2:** Separar la raíz",
        "$$\\sqrt{50} = \\sqrt{25 \\times 2} = \\sqrt{25} \\cdot \\sqrt{2}$$",
        "",
        "**Paso 3:** Simplificar",
        "$$\\sqrt{25} \\cdot \\sqrt{2} = 5\\sqrt{2}$$",
        "",
        "✅ **$5\\sqrt{2}$**"
      ],
      "explanation": "50 = 25×2, entonces √50 = √25·√2 = 5√2"
    },
    {
      "id": "onr-003",
      "topic": "orden-operaciones",
      "question": "Evalúa: $3 + 2 \\times 5^2 - 4$",
      "type": "numeric",
      "correct": 49,
      "tolerance": 0,
      "difficulty": "medio",
      "hints": [
        "Orden: PEMDAS (Paréntesis, Exponentes, Mult/Div, Suma/Resta)",
        "Primero: 5² = 25",
        "Luego: 2×25 = 50, después 3+50-4"
      ],
      "stepByStep": [
        "📚 **Orden de Operaciones - PEMDAS**",
        "",
        "**P**aréntesis, **E**xponentes, **M**ultiplicación/**D**ivisión, **S**uma/Resta",
        "",
        "**Expresión:** $3 + 2 \\times 5^2 - 4$",
        "",
        "**Paso 1: Exponentes**",
        "$$3 + 2 \\times 25 - 4$$",
        "",
        "**Paso 2: Multiplicación**",
        "$$3 + 50 - 4$$",
        "",
        "**Paso 3: Suma y Resta (izq a der)**",
        "$$53 - 4 = 49$$",
        "",
        "✅ **49**"
      ],
      "explanation": "Primero exponente (5²=25), luego multiplicación (2×25=50), finalmente suma y resta: 3+50-4=49"
    },
    {
      "id": "onr-004",
      "topic": "fracciones-decimales",
      "question": "Convierte a fracción: $0.75$",
      "type": "multiple-choice",
      "shuffle": true,
      "options": [
        "$\\frac{3}{4}$",
        "$\\frac{75}{10}$",
        "$\\frac{7}{5}$",
        "$\\frac{15}{20}$"
      ],
      "correct": 0,
      "difficulty": "facil",
      "hints": [
        "0.75 = 75/100",
        "Simplifica dividiendo entre el MCD",
        "75 y 100 se dividen entre 25"
      ],
      "stepByStep": [
        "🔄 **Decimal a Fracción**",
        "",
        "**Paso 1:** Escribir sobre potencia de 10",
        "$$0.75 = \\frac{75}{100}$$",
        "",
        "**Paso 2:** Simplificar (MCD = 25)",
        "$$\\frac{75 \\div 25}{100 \\div 25} = \\frac{3}{4}$$",
        "",
        "✅ **$\\frac{3}{4}$**"
      ],
      "explanation": "0.75 = 75/100, simplificando entre 25: 3/4"
    }
  ]
}