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(6x^4y^3)^2

2 min read Jun 16, 2024
(6x^4y^3)^2

Simplifying (6x^4y^3)^2

This article will walk through the process of simplifying the expression (6x^4y^3)^2.

Understanding the Concepts

  • Exponent: An exponent indicates how many times a base number is multiplied by itself. For example, x^2 means x multiplied by itself twice (x*x).
  • Power of a product: When a product is raised to a power, each factor within the product is raised to that power. For example, (ab)^2 = a^2 * b^2.
  • Power of a power: When a power is raised to another power, the exponents are multiplied. For example, (x^2)^3 = x^(2*3) = x^6.

Simplifying the Expression

  1. Apply the power of a product rule: We can distribute the exponent of 2 to each factor within the parentheses: (6x^4y^3)^2 = 6^2 * (x^4)^2 * (y^3)^2

  2. Apply the power of a power rule: Simplify the exponents: 6^2 * (x^4)^2 * (y^3)^2 = 36 * x^(42) * y^(32)

  3. Simplify the exponents: 36 * x^(42) * y^(32) = 36x^8y^6

Conclusion

Therefore, the simplified expression for (6x^4y^3)^2 is 36x^8y^6.

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