## Simplifying Expressions with Exponents: (x^3y^7)^2

In mathematics, understanding how to manipulate exponents is crucial for simplifying complex expressions. One common scenario involves raising an entire expression with exponents to another power. Let's delve into simplifying the expression **(x^3y^7)^2**.

### The Power of a Power Rule

The fundamental rule we need here is the **power of a power rule**: **(a^m)^n = a^(m*n)**. This rule states that when raising a power to another power, you multiply the exponents.

### Applying the Rule to Our Expression

Let's apply this rule to our expression (x^3y^7)^2:

**Apply the power of a power rule:**(x^3y^7)^2 = x^(3*2) * y^(7*2)**Simplify the exponents:**x^(3*2) * y^(7*2) = x^6 * y^14

### Final Result

Therefore, the simplified form of (x^3y^7)^2 is **x^6 * y^14**.

### Key Takeaway

By understanding the power of a power rule and applying it correctly, we can efficiently simplify complex expressions involving exponents. This rule is a valuable tool in algebra and beyond, enabling us to manipulate expressions with ease.