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 Expone...
• 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
#MathOlympiad #ExponentialEquations #MathTutorial #SciMarvels #AdvancedMath #ProblemSolving #MathCompetition #Algebra #MathSkills #LearnMath #MathWithoutVoice #Educational #MathVideos #STEM #ScienceEducation #MathHelp #Mathematics #OlympiadPreparation #HighSchoolMath #MathCompetitions #MathChallenge #MathPractice #MathConcepts #AlgebraicEquations #LearningMathematics #MathSolutions #CompetitiveMath #MathExamPrep #ScientificProblems #MathStrategies , Math Olympiad, STEM Olympiad, Competition Math, Problem Solving, Critical Thinking, Geometry, Calculus, Beginner Olympiad Problems, Intermediate Olympiad Problems, Advanced Olympiad Problems, IMO, Math Circles,Math Competitions,Math Puzzles,STEM Challenges,Proof Techniques,exponential equations, solving exponential equations, exponential equation,olympiad mathematics, algebra,math olympiad question, Exponential Fractions, Scimarvels, step-by-step tutorial, (21^63)/(63^21) , Mathematical Tricks , Mathematical problem

[@yosefsalehi-bh2zy]

That was Impressive

[@Sci-Marvels]

Thanks Yosef 🙂

[@fatemetahernezhad]

That's on point

[@Sci-Marvels]

Bravo Fatemeh

[@yosefsalehi-bh2zy]

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[@Sci-Marvels]

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