BT Lecture 07 | Hacks to find Remainder for questions of type 32^32^32 divided by 9 | JEE mains 2026

Find the remainder when 32^32^32 is divided by 9 Find the remainder when 2025^2024^2023 is divided by 7 This lecture focuses on hacks to find remainders for complex exponent questions commonly seen in JEE Mains exams, specifically those with powers stacked on top of each other, like $32^{32^{32}}$ divided by 9 (3:30). The video covers: Introduction to complex remainder problems (1:17) and how they differ from simpler "reverse Pushpa" type questions. Methodology for solving such problems (4:17): Step 1: Simplify the base by finding its remainder when divided by the given divisor (4:30). Step 2: Analyze the cyclicity of the simplified base's powers with respect to the divisor (7:31). This helps determine the pattern of remainders. Step 3: Determine the type of the exponent (e.g., $3m$, $3m+1$, $3m+2$) by dividing it by the cycle length found in Step 2. This often involves applying remainder rules to the exponent itself (9:39). Step 4: Use the exponent's type to find the final remainder based on the cyclicity pattern (10:12). Examples and practice problems (3:48, 12:31, 16:53): The lecture walks through two main examples: $32^{32^{32}}$ divided by 9 (3:26). $2025^{2024^{2023}}$ divided by 7 (12:31). A third, simpler example of $32^{32 times 32}$ divided by 9 is also discussed to differentiate it from the stacked power problem (16:53). Emphasis on understanding patterns and concepts (11:36, 12:27) rather than rote memorization. #JEEMain2026 #JEEMains #JEE2026 #JEEMaths #MathsShortcuts #ShortcutSeries #IITJEEPreparation #JEETricks #FastMaths #PCMStudents #AnantyamMaths #pyqs #pyqseries For more videos, subscribe https://www.youtube.com/c/AVsAnantyam... 00:00 Intro 01:17 Introduction to complex remainder problems 03:26 Find the remainder when 32^32^32 is divided by 9 12:31 Find the remainder when 2025^2024^2023 is divided by 7 18:40 Outro 16:53 Find the remainder when (32^32)^32 is divided by 9