Welcome to SciMarvels! In this video, we tackle a challenging math Olympiad problem involving the simplification of advanced exponential fraction. 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: (40^40) / (20^20) = ?
1. Express 40 and 20 in terms of their prime factors:
o 40 = 2^3 * 5
o 20 = 2^2 * 5
2. Rewrite the given problem using these expressions:
o (40^40) / (20^20)
o ( (2^3 * 5)^40 ) / ( (2^2 * 5)^20 )
3. Simplify the exponents:
o (2^(340) * 5^40) / (2^(220) * 5^20)
o (2^120 * 5^40) / (2^40 * 5^20)
4. Separate the fractions:
o (2^120 / 2^40) * (5^40 / 5^20)
5. Simplify each fraction:
o 2^(120-40) * 5^(40-20)
o 2^80 * 5^20
6. Combine the simplified terms:
o (2^80) * (2^40 * 20^20 / 2^20 * 20^20)
o 2^(60) * 20^20
o 2^20 * 2 * 2 * 2^20 = 2^40
7. Rewrite the expression as:
o 80^20
Therefore, the simplified expression is: 80^20
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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 Solve Complex E...
• How to Simplify Expone...
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✅ Why Subscribe to SciMarvels?
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:
Exponential Equations, Algebra, Math Tutorials, Educational Math Videos, Fun Learning, SciMarvels Channel, Math Without Voiceover, Visual Learning, Exponent Rules, Algebraic Simplification, KZitem Math, Math Education, Algebra Techniques, Interactive Math, Science and Math Fun, Algebraic Solutions, Silent Math Tutorial, Educational Content, (40^40) / (20^20)
Негізгі бет How to Simplify Exponential Fraction 40^40/20^20 | Math Olympiad Problem | New Magic Tricks
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