(5x^3y^4)^2

less than a minute read Jun 16, 2024
(5x^3y^4)^2

Simplifying (5x^3y^4)^2

In mathematics, simplifying expressions often involves applying rules of exponents. Let's break down how to simplify the expression (5x^3y^4)^2.

Understanding the Power of a Product Rule

The key to solving this is the power of a product rule, which states: (ab)^n = a^n * b^n. This means that when raising a product to a power, we can raise each factor to that power.

Applying the Rule

  1. Apply the power of a product rule: (5x^3y^4)^2 = 5^2 * (x^3)^2 * (y^4)^2

  2. Simplify the exponents:

    • 5^2 = 25
    • (x^3)^2 = x^(3*2) = x^6
    • (y^4)^2 = y^(4*2) = y^8
  3. Combine the terms: 25x^6y^8

Final Result

Therefore, the simplified form of (5x^3y^4)^2 is 25x^6y^8.

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