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(2x^5)^2(3x^2)^3

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

Simplifying Algebraic Expressions: (2x^5)^2(3x^2)^3

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

Understanding the Properties of Exponents

Before we begin simplifying, let's review some key exponent properties:

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

Simplifying the Expression

  1. Apply the Power of a Power Property:

    • (2x^5)^2 = 2^2 * (x^5)^2 = 4x^10
    • (3x^2)^3 = 3^3 * (x^2)^3 = 27x^6

  2. Substitute the simplified terms back into the original expression:

    • (2x^5)^2(3x^2)^3 = 4x^10 * 27x^6

  3. Apply the Product of Powers Property:

    • 4x^10 * 27x^6 = (4 * 27) * (x^10 * x^6) = 108x^16

Final Answer

Therefore, the simplified form of the expression (2x^5)^2(3x^2)^3 is 108x^16.

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