This study explores the relationship between knowledge elements in the Teachers' AI-TPACK framework, aiming to construct a model that clarifies the complex interplay between AI technology, pedagogical methods, and subject-specific content in education. The AI-TPACK framework includes seven components: Pedagogical Knowledge (PK), Content Knowledge (CK), AI-Technological Knowledge (AI-TK), Pedagogical Content Knowledge (PCK), AI-Technological Pedagogical Knowledge (AI-TCK), AI-Technological Content Knowledge (AI-TPK), and AI-TPACK itself. Using exploratory factor analysis (EFA) and confirmatory factor analysis (CFA), the study investigates the relationships among these knowledge elements. The results show that six knowledge elements serve as predictive factors for AI-TPACK variables, with varying levels of explanatory power. Core knowledge elements (PK, CK, and AI-TK) influence AI-TPACK indirectly, mediated by composite elements (PCK, AI-TCK, and AI-TPK). Non-technical knowledge elements have significantly lower explanatory power compared to technical elements. Content knowledge (CK) diminishes the explanatory power of PCK and AI-TCK. The study provides a comprehensive framework for assessing teachers' AI-TPACK and highlights the importance of understanding the interplay among AI-TPACK elements for effective AI integration in education. The findings suggest that AI-TPACK is a hierarchical model, with core knowledge elements at the first level and composite elements at the second level, where the most significant impact on AI-TPACK comes from AI-TPK. The study underscores the need for further research to refine the AI-TPACK framework and enhance the understanding of AI's role in education.This study explores the relationship between knowledge elements in the Teachers' AI-TPACK framework, aiming to construct a model that clarifies the complex interplay between AI technology, pedagogical methods, and subject-specific content in education. The AI-TPACK framework includes seven components: Pedagogical Knowledge (PK), Content Knowledge (CK), AI-Technological Knowledge (AI-TK), Pedagogical Content Knowledge (PCK), AI-Technological Pedagogical Knowledge (AI-TCK), AI-Technological Content Knowledge (AI-TPK), and AI-TPACK itself. Using exploratory factor analysis (EFA) and confirmatory factor analysis (CFA), the study investigates the relationships among these knowledge elements. The results show that six knowledge elements serve as predictive factors for AI-TPACK variables, with varying levels of explanatory power. Core knowledge elements (PK, CK, and AI-TK) influence AI-TPACK indirectly, mediated by composite elements (PCK, AI-TCK, and AI-TPK). Non-technical knowledge elements have significantly lower explanatory power compared to technical elements. Content knowledge (CK) diminishes the explanatory power of PCK and AI-TCK. The study provides a comprehensive framework for assessing teachers' AI-TPACK and highlights the importance of understanding the interplay among AI-TPACK elements for effective AI integration in education. The findings suggest that AI-TPACK is a hierarchical model, with core knowledge elements at the first level and composite elements at the second level, where the most significant impact on AI-TPACK comes from AI-TPK. The study underscores the need for further research to refine the AI-TPACK framework and enhance the understanding of AI's role in education.