How to Use Mathematical Tricks for Simplifying Exponential Fraction | Step-by-step Tutorial

Welcome to SciMarvels! In this video, we tackle a challenging math Olympiad problem involving the simplification of advanced exponential equations. Watch as we solve the problem step-by-step on paper, providing a clear and detailed explanation without any voiceover. This unique approach allows you to focus entirely on the math and understand the process visually.
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✅ Key Concepts Covered
• Exponential Equations
• Algebraic Manipulations
• Problem-Solving Strategies
• Mathematical Simplification
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✅ Detailed Steps
We begin with the problem: (21^63) / (63^21) = ?
1. Express 63 in terms of its prime factors:
o 63 = 3 * 21
2. Rewrite the given problem using these expressions:
o (21^63) / (63^21)
o (21^63) / ((3 * 21)^21)
3. Simplify the denominator:
o (21^63) / (3^21 * 21^21)
4. Separate the fractions:
o (21^63) / (3^21 * 21^21)
o (21^63) / 3^21 / 21^21
5. Simplify the exponents:
o 21^(63 - 21) / 3^21
o 21^42 / 3^21
6. Express 21 as its prime factors:
o 21 = 3 * 7
7. Rewrite the problem using these expressions:
o (3 * 7)^42 / 3^21
8. Simplify the numerator:
o 3^42 * 7^42 / 3^21
9. Separate the fractions:
o (3^42 / 3^21) * 7^42
o 3^(42 - 21) * 7^42
o 3^21 * 7^42
10. Combine the terms:
o (3 * 7)^21
11. Simplify the final expression:
o 21^21 * 7^21
Therefore, the simplified expression is: 147^21
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✅ Learning Outcomes
By the end of this video, you will:
• Understand how to manipulate and simplify exponential equations.
• Gain skills in algebraic manipulation and problem-solving strategies.
• Enhance your mathematical simplification techniques for advanced problems.
• Develop a deeper understanding of how to approach and solve complex math problems.
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✅ Also you can see:
   • How to Simplify Exponential Fraction ...  
   • How to Simplify Exponential Equations...  
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At SciMarvels, we are dedicated to making complex math and physics problems accessible and enjoyable. Our unique approach of solving problems without voiceovers allows you to concentrate solely on the math, fostering a deeper understanding. Subscribe to join a community of learners who are passionate about mastering scientific concepts through clear, step-by-step solutions.
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✅ Tags
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