(x^4y^3)^2

2 min read Jun 17, 2024
(x^4y^3)^2

Simplifying (x^4y^3)^2

In mathematics, simplifying expressions is a fundamental skill. This article will guide you through the process of simplifying the expression (x^4y^3)^2.

Understanding the Laws of Exponents

To tackle this expression, we need to understand the following laws of exponents:

  • Product of powers: x^m * x^n = x^(m+n)
  • Power of a product: (x * y)^n = x^n * y^n
  • Power of a power: (x^m)^n = x^(m*n)

Simplifying the Expression

Let's break down the simplification step-by-step:

  1. Apply the power of a product rule: (x^4y^3)^2 = (x^4)^2 * (y^3)^2

  2. Apply the power of a power rule: (x^4)^2 * (y^3)^2 = x^(42) * y^(32)

  3. Simplify: x^(42) * y^(32) = x^8y^6

Conclusion

Therefore, the simplified form of (x^4y^3)^2 is x^8y^6. This process demonstrates how to use the laws of exponents to simplify expressions involving powers of variables.

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