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Simplifying Algebraic Expressions: (5x³y⁻⁵)(4xy³)
This article will guide you through simplifying the algebraic expression **(5x³y⁻⁵)(4xy³) **.
Understanding the Basics
Before we begin, let's recall some fundamental rules of exponents:
- Product of Powers: When multiplying exponents with the same base, add their powers: xᵃ * xᵇ = xᵃ⁺ᵇ
- Negative Exponent: Any term raised to a negative exponent is equal to its reciprocal with a positive exponent: x⁻ᵃ = 1/xᵃ
Simplifying the Expression
- Combine the coefficients: Multiply the numerical coefficients: 5 * 4 = 20
- Combine x terms: Apply the Product of Powers rule to the x terms: x³ * x¹ = x³⁺¹ = x⁴
- Combine y terms: Apply the Product of Powers rule to the y terms: y⁻⁵ * y³ = y⁻⁵⁺³ = y⁻²
- Simplify the negative exponent: Apply the Negative Exponent rule to the y term: y⁻² = 1/y²
Final Result
Putting it all together, the simplified expression is: 20x⁴/y²
Therefore, (5x³y⁻⁵)(4xy³) = 20x⁴/y².
Key Takeaways
- Remember the rules of exponents when dealing with algebraic expressions.
- Simplifying expressions can make them easier to work with.
- Practice applying the rules to different expressions to improve your understanding.