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(4x^3y^5)^2

2 min read Jun 16, 2024
(4x^3y^5)^2

Simplifying the Expression (4x^3y^5)^2

This article will guide you through the process of simplifying the expression (4x^3y^5)^2.

Understanding the Concepts

  • Exponents: An exponent indicates how many times a base number is multiplied by itself. In this case, the base is (4x^3y^5) and the exponent is 2.
  • Power of a Product: When raising a product to a power, you raise each factor in the product to that power. This means we need to apply the exponent 2 to both 4 and the variables x^3 and y^5.

The Simplification Process

  1. Distribute the exponent: Apply the exponent 2 to each factor inside the parentheses.

    (4x^3y^5)^2 = 4^2 * (x^3)^2 * (y^5)^2

  2. Simplify the exponents: Remember that when raising a power to another power, you multiply the exponents.

    4^2 * (x^3)^2 * (y^5)^2 = 16 * x^(32) * y^(52)

  3. Calculate the final result:

    16 * x^(32) * y^(52) = 16x^6y^10

Conclusion

Therefore, the simplified form of the expression (4x^3y^5)^2 is 16x^6y^10. By understanding the rules of exponents, you can effectively simplify complex expressions and arrive at a concise result.

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