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(x^2y^5)^3

less than a minute read Jun 17, 2024
(x^2y^5)^3

Simplifying (x^2y^5)^3

In mathematics, simplifying expressions is an essential skill. One common type of simplification involves expressions with exponents. Let's take a look at how to simplify the expression (x^2y^5)^3.

Understanding the Rules

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

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

Applying the Rules

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

  2. Apply the power of a power rule: (x^2)^3 * (y^5)^3 = x^(23) * y^(53)

  3. Simplify the exponents: x^(23) * y^(53) = x^6 * y^15

Final Result

Therefore, the simplified form of (x^2y^5)^3 is x^6y^15.

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