(2xy^5)^3

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

Simplifying (2xy^5)^3

In mathematics, simplifying expressions is a key skill. Let's break down how to simplify the expression (2xy^5)^3.

Understanding the Rules

The key to this simplification lies in the power of a product and the power of a power rules.

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

Applying the Rules

  1. Apply the power of a product rule: (2xy^5)^3 = 2^3 * x^3 * (y^5)^3

  2. Apply the power of a power rule: 2^3 * x^3 * (y^5)^3 = 2^3 * x^3 * y^(5*3)

  3. Simplify the exponents: 2^3 * x^3 * y^(5*3) = 8x^3y^15

The Final Result

Therefore, the simplified form of (2xy^5)^3 is 8x^3y^15.

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