(x^3y^5)^4(x^3y^2)^-2

Jasonbradley

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Jun 17, 2024

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Simplifying Expressions with Exponents

This article will guide you through simplifying the expression (x³y⁵)⁴(x³y²)⁻². We'll break down the process step-by-step using the rules of exponents.

Understanding the Rules

Before we begin, let's review the key exponent rules that we'll use:

• Product of powers: xᵃ * xᵇ = xᵃ⁺ᵇ
• Power of a power: (xᵃ)ᵇ = xᵃᵇ
• Negative exponent: x⁻ᵃ = 1/xᵃ

Simplifying the Expression

1. Apply the Power of a Power Rule:

   • (x³y⁵)⁴ = x³⁴ y⁵⁴ = x¹²y²⁰
   • (x³y²)⁻² = x³*⁻² y²*⁻² = x⁻⁶y⁻⁴

2. Substitute the simplified terms back into the original expression:

   • (x¹²y²⁰)(x⁻⁶y⁻⁴)

3. Apply the Product of Powers Rule:

   • x¹² * x⁻⁶ = x¹²⁻⁶ = x⁶
   • y²⁰ * y⁻⁴ = y²⁰⁻⁴ = y¹⁶

4. Combine the results:

   • x⁶y¹⁶

Final Result

The simplified form of (x³y⁵)⁴(x³y²)⁻² is x⁶y¹⁶.