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

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

Simplify the exponents:
 5^2 = 25
 (x^3)^2 = x^(3*2) = x^6
 (y^4)^2 = y^(4*2) = y^8

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