(6x^3y^5)^2

2 min read Jun 16, 2024
(6x^3y^5)^2

Simplifying (6x³y⁵)²

In mathematics, simplifying expressions is a crucial skill. Let's break down how to simplify the expression (6x³y⁵)².

Understanding the Concept

The expression involves a power of a product, meaning we have a product of terms raised to a power. The rule for simplifying this type of expression is:

(ab)² = a²b²

This rule essentially states that we can distribute the exponent to each term within the parentheses.

Applying the Rule

  1. Distribute the exponent: (6x³y⁵)² = 6² (x³)² (y⁵)²

  2. Simplify the exponents: 6² (x³)² (y⁵)² = 36x⁶y¹⁰

Final Answer

Therefore, the simplified form of (6x³y⁵)² is 36x⁶y¹⁰.

Key Points to Remember

  • When raising a power to another power, multiply the exponents: (a^m)^n = a^(m*n).
  • The exponent applies to every term inside the parentheses.
  • Pay attention to the order of operations: exponents are performed before multiplication.

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