## 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.