## Simplifying (5xy^2)^4

In mathematics, simplifying expressions often involves applying the rules of exponents. One such rule states that **when raising a product to a power, we raise each factor to that power**. Let's break down the simplification of **(5xy^2)^4**.

### Applying the Rule

**(5xy^2)^4 = 5^4 * x^4 * (y^2)^4**

Here, we've raised each factor (5, x, and y^2) to the power of 4.

### Simplifying Further

**5^4 * x^4 * (y^2)^4 = 625x^4y^8**

We've simplified 5^4 to 625 and applied another rule of exponents: **(a^m)^n = a^(m*n)**. This gives us (y^2)^4 = y^(2*4) = y^8.

### The Final Answer

Therefore, the simplified form of (5xy^2)^4 is **625x^4y^8**.