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(5x^3y)^2(-2x^5y^1)

2 min read Jun 16, 2024
(5x^3y)^2(-2x^5y^1)

Simplifying Algebraic Expressions: (5x^3y)^2(-2x^5y^1)

This article will guide you through the process of simplifying the algebraic expression (5x^3y)^2(-2x^5y^1).

Understanding the Rules

Before we begin, let's recall some essential rules of exponents:

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

Step-by-Step Simplification

  1. Simplify the first term:

    • (5x^3y)^2 = 5^2 * (x^3)^2 * y^2 = 25x^6y^2

  2. Simplify the second term:

    • (-2x^5y^1) remains as it is.

  3. Multiply the simplified terms:

    • 25x^6y^2 * (-2x^5y^1) = -50x^(6+5)y^(2+1)

  4. Combine the exponents:

    • -50x^(6+5)y^(2+1) = -50x^11y^3

Final Result

Therefore, the simplified form of the expression (5x^3y)^2(-2x^5y^1) is -50x^11y^3.

Key Points

  • Remember the order of operations (PEMDAS/BODMAS) when dealing with expressions.
  • Pay close attention to the signs of the coefficients.
  • Always simplify expressions to their simplest form.

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