%5E2(2xy%5E3z)%5E3(4xyz).jpeg "(5x^2y)^2(2xy^3z)^3(4xyz)")
Simplifying Algebraic Expressions: A Step-by-Step Guide
This article will guide you through simplifying the algebraic expression: (5x²y)²(2xy³z)³(4xyz). We'll break down the process into manageable steps to ensure clarity.
Understanding the Rules of Exponents
Before diving into the simplification, let's refresh our memory on some crucial exponent rules:
- Product of powers: x^m * x^n = x^(m+n)
- Power of a product: (xy)^n = x^n * y^n
- Power of a power: (x^m)^n = x^(m*n)
Simplifying the Expression
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Apply the power of a product rule:
- (5x²y)² = 5² * (x²)² * y² = 25x⁴y²
- (2xy³z)³ = 2³ * x³ * (y³)³ * z³ = 8x³y⁹z³
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Substitute the simplified terms back into the original expression:
- 25x⁴y² * 8x³y⁹z³ * 4xyz
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Rearrange the terms for easier multiplication:
- 25 * 8 * 4 * x⁴ * x³ * x * y² * y⁹ * y * z³ * z
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Apply the product of powers rule:
- 800x⁸y¹²z⁴
Final Answer
Therefore, the simplified form of the expression (5x²y)²(2xy³z)³(4xyz) is 800x⁸y¹²z⁴.
Key Takeaways
- Understanding exponent rules is crucial for simplifying algebraic expressions.
- Break down complex expressions into smaller, manageable parts.
- Apply the rules of exponents systematically to arrive at the final solution.
Remember, practice makes perfect! The more you work with algebraic expressions, the more comfortable you'll become with simplifying them.