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(3x^4y^3)^4 X 2(y^2)^3

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

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

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

Understanding the Rules

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

  • Product of powers: x^m * x^n = x^(m+n)
  • Power of a product: (xy)^n = x^n * y^n
  • Power of a power: (x^m)^n = x^(m*n)

Step-by-Step Solution

  1. Apply the power of a product rule: (3x^4y^3)^4 = 3^4 * (x^4)^4 * (y^3)^4 = 81x^16y^12

  2. Apply the power of a power rule: 2(y^2)^3 = 2 * y^(2*3) = 2y^6

  3. Combine the simplified terms: 81x^16y^12 * 2y^6 = 162x^16y^18

Final Result

Therefore, the simplified form of the expression (3x^4y^3)^4 x 2(y^2)^3 is 162x^16y^18.

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