You are a highly experienced educational content creator  for Indian competitive exams such as Railway (Typist - Non_Technical_Posts) under the subject of Mathematics. The topic is **Number System**.. Your task is to generate a detailed **bilingual explanation (English + Hindi)** for a **mnemonic anagram letter** for topic Number System, using the following inputs.

    Generate a Markdown output using this structure:

    ---

    🧠 **Anagram (Short)**: DIVERSES  
    📖 **Expanded (English)**: Diverse Important Various Essential Rational Subtopics Encompassing Simple Elements  
    📖 **Expanded (Hindi)**: विविध महत्वपूर्ण विभिन्न आवश्यक तार्किक उपविषय सरल तत्वों को समेटे हुए

    ---

    ### 🔠 Letter: I / इ — *Indices and Powers / घातांक और शक्ति*

    #### 📚 Concept:
    - EN: Indices and Powers  
    - HI: घातांक और शक्ति

    #### 🧠 Type:
    - EN: Indices and Powers  
    - HI: घातांक और शक्ति

    #### 📖 Description:
    - EN: Handling problems involving exponents, powers, and laws of indices.  
    - HI: घातांक, शक्तियों और घातांक नियमों से जुड़ी समस्याओं को हल करना।

    #### 📌 Explanation:
    - EN: Indices represent repeated multiplication. Laws of indices simplify operations on powers like multiplication, division, and raising powers to powers.  
    - HI: घातांक गणना को दोहराए गए गुणन के रूप में दर्शाते हैं। घातांकों के नियम शक्तियों पर ऑपरेशन को सरल बनाते हैं जैसे गुणा, भाग, और शक्तियों को घात देने।

    #### ➗ Formula or Relation:
    - EN: **a^m × a^n = a^(m+n), (a^m)^n = a^(m×n)**  
    - HI: **a^m × a^n = a^(m+n), (a^m)^n = a^(m×n)**

    #### 💡 Example Questions:
    **ENGLISH:**
    ['If a number is expressed as 3^4 × 5^3, find the value of the number raised to the power 2. Using the laws of indices, calculate the final result and determine if it is divisible by 5^5.', 'A data packet size increases exponentially where each level is multiplied by 2^n. If the initial size is 128 KB and after 5 levels, find the total size. Demonstrate your calculation using indices laws.', 'Evaluate the expression (9^3 × 27^2) ÷ (3^5) using laws of indices. Show detailed stepwise simplification and final value.']

    **HINDI:**
    ['यदि कोई संख्या 3^4 × 5^3 के रूप में व्यक्त है, तो उस संख्या का वर्गमूल निकालें। घातांक के नियमों का उपयोग करके अंतिम परिणाम ज्ञात करें और पता लगाएं कि क्या वह संख्या 5^5 से विभाजित है।', 'एक डाटा पैकेट का आकार एक्सपोनेंशियल बढ़ता है जहाँ प्रत्येक स्तर 2^n से गुणा होता है। प्रारंभिक आकार 128 KB है, 5 स्तरों के बाद कुल आकार ज्ञात करें। घातांक नियमों का उपयोग करके गणना दिखाएं।', 'व्यंजक (9^3 × 27^2) ÷ (3^5) का मान निकालें। घातांक नियमों का उपयोग करके चरणबद्ध सरलीकरण और अंतिम मान दिखाएं।']

    ---
    object should have:
        - "mnemonic_letter_english", "mnemonic_letter_hindi"
        - "type_english", "type_hindi"
        - "description_english", "description_hindi"
        - "difficulty_level_english", "difficulty_level_hindi"
        - "exam_frequency_english", "exam_frequency_hindi"
        - "time_to_solve_english", "time_to_solve_hindi"
        - "clue_words_english": list of 4-5 identifying keywords/phrases
        - "clue_words_hindi": same in Hindi
        - "what_to_use_english", "what_to_use_hindi"
        - "formula_english", "formula_hindi"
        - "alternative_formulas_english", "alternative_formulas_hindi": list of 2-3 alternative formulas
        - "algorithm_english", "algorithm_hindi": step-by-step string list
        - "quick_method_english", "quick_method_hindi"

        - "example": answer all  the question give as Example Questions.
 
          - Require multi-step calculation or reasoning.
          - NOT be short phrases, fragments, or simplified school-level word problems.each Example Questions should be including:
            - "example_no"
            - "question_english", "question_hindi"
            - "solution_steps_english": step list
            - "solution_steps_hindi": step list
            - "answer_english", "answer_hindi"
            - "verification_english", "verification_hindi"

        - "variations_english", "variations_hindi": list of variation types
        - "related_concepts_english", "related_concepts_hindi": related subtopics or concepts
        - "common_mistakes_english", "common_mistakes_hindi": list of 10 traps or errors
        - "tip_english", "tip_hindi": short-cut or important tip
        - "prerequisite_knowledge_english", "prerequisite_knowledge_hindi": list of 3 concepts
        - "practice_problems_english", "practice_problems_hindi": list of 3  full-length and detailed practical, compact competitive-level example questions** per type.  
      ⚠️ NOTE : Ensure answer all the question of Example Questions in the example key

        Use simple, learner-friendly language and return only the JSON object in your response, formatted with proper indentation and structure.
        Use clear language suitable for aptitude learners and format the JSON cleanly

### 🔁 output JSon should be

```json
            { 
              "mnemonic_letter_english": "",
              "mnemonic_letter_hindi": "",
              "type_english": "",
              "type_hindi": "",
              "description_english": "",
              "description_hindi": "",
              "difficulty_level_english": "",
              "difficulty_level_hindi": "",
              "exam_frequency_english": "",
              "exam_frequency_hindi": "",
              "time_to_solve_english": "",
              "time_to_solve_hindi": "",
              "clue_words_english": [
                  "",
                  "",
                  "",
                  "",
                  ""
              ],
              "clue_words_hindi": [
                  "",
                  "",
                  "",
                  "",
                  ""
              ],
              "what_to_use_english": "",
              "what_to_use_hindi": "",
              "formula_english": "",
              "formula_hindi": "",
              "alternative_formulas_english": [
                  "",
                  ""
              ],
              "alternative_formulas_hindi": [
                  "",
                  ""
              ],
              "algorithm_english": [
                  "",
                  "",
                  "",
                  ""
              ],
              "algorithm_hindi": [
                  "",
                  "",
                  "",
                  ""
              ],
              "quick_method_english": "",
              "quick_method_hindi": "",
              "example": [
                  {
                  "example_no":"",
                  "question_english": "",
                  "question_hindi": "",
                  "solution_steps_english": [
                      "",
                      "",
                      "",
                      "",
                      ""
                  ],
                  "solution_steps_hindi": [
                      "",
                      "",
                      "",
                      "",
                      ""
                  ],
                  "answer_english": "",
                  "answer_hindi": "",
                  "verification_english": "",
                  "verification_hindi": ""
              }..,],
              "variations_english": [
                  "",
                  "",
                  ""
              ],
              "variations_hindi": [
                  "",
                  "",
                  ""
              ],
              "related_concepts_english": [
                  "",
                  "",
                  ""
              ],
              "related_concepts_hindi": [
                  "",
                  "",
                  ""
              ],
              "common_mistakes_english": [
                  "",
                  ""
              ],
              "common_mistakes_hindi": [
                  "",
                  ""
              ],
              "tip_english": "",
              "tip_hindi": "",
              "prerequisite_knowledge_english": [
                  "",
                  "",
                  ""
              ],
              "prerequisite_knowledge_hindi": [
                  "",
                  "",
                  ""
              ],
              "practice_problems_english": [
                  "",
                  ""
              ],
              "practice_problems_hindi": [
                  "",
                  ""
              ]
          }