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(5xy^2)^2(3x^3y)

less than a minute read Jun 16, 2024
(5xy^2)^2(3x^3y)

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

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

Understanding the Rules

To simplify this expression, we need to apply the following rules of exponents:

  • Power of a product: (ab)^n = a^n * b^n
  • Product of powers: a^m * a^n = a^(m+n)

Simplifying the Expression

  1. Simplify the first part:

    • (5xy^2)^2 = 5^2 * x^2 * (y^2)^2 = 25x^2y^4

  2. Combine with the second part:

    • 25x^2y^4 * 3x^3y

  3. Apply the product of powers rule:

    • 25 * 3 * x^(2+3) * y^(4+1) = 75x^5y^5

Final Answer

Therefore, the simplified expression for (5xy^2)^2(3x^3y) is 75x^5y^5.

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