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

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

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

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

Understanding the Rules

To simplify this expression, we'll need to use the following rules of exponents:

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

Step-by-Step Simplification

  1. Apply the Power of a Product rule to the first term: (2x^2y^3)^3 = 2^3 * (x^2)^3 * (y^3)^3

  2. Simplify using the Power of a Power rule: 2^3 * (x^2)^3 * (y^3)^3 = 8x^6y^9

  3. Multiply the simplified first term by the second term: 8x^6y^9 * (xy^2) = 8x^(6+1)y^(9+2)

  4. Simplify the exponents: 8x^(6+1)y^(9+2) = 8x^7y^11

Final Answer

Therefore, the simplified form of the expression (2x^2y^3)^3(xy^2) is 8x^7y^11.

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