## Understanding (x^2y)^5

In mathematics, expressions involving exponents often require careful simplification. Let's break down the expression **(x^2y)^5** and understand its meaning.

### The Power of a Product Rule

The core principle at play here is the **power of a product rule**. This rule states that when raising a product to a power, we raise each factor in the product to that power.

In our case:

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

### Simplifying the Exponents

Now we have two separate terms with exponents:

**(x^2)^5**: When raising a power to another power, we multiply the exponents. So, (x^2)^5 = x^(2*5) = x^10**(y)^5**: This term remains as y^5

### The Final Result

Combining the simplified terms, we get the final simplified expression:

**(x^2y)^5 = x^10y^5**

### Key Takeaways

- The power of a product rule is crucial for simplifying expressions with exponents.
- When raising a power to another power, we multiply the exponents.
- Simplifying expressions helps us understand their values and perform further calculations more easily.