(6x^4y^5)^5

Jasonbradley

2 min read

·

Jun 16, 2024

11

Share

Simplifying Expressions with Exponents: (6x^4y^5)^5

In mathematics, simplifying expressions often involves understanding the rules of exponents. One such expression is (6x^4y^5)^5. Let's break down how to simplify this expression step by step.

Understanding the Rules

• Power of a Product: When a product is raised to a power, each factor within the product is raised to that power.
• Power of a Power: When a power is raised to another power, the exponents are multiplied.

Applying the Rules to (6x^4y^5)^5

1. Apply the Power of a Product Rule:

   • (6x^4y^5)^5 = 6^5 * (x^4)^5 * (y^5)^5

2. Apply the Power of a Power Rule:

   • 6^5 * (x^4)^5 * (y^5)^5 = 6^5 * x^(45) * y^(55)

3. Simplify the Exponents:

   • 6^5 * x^(45) * y^(55) = 7776 * x^20 * y^25

Final Simplified Expression

Therefore, the simplified form of (6x^4y^5)^5 is 7776x^20y^25.