## Simplifying (a^2)^3

In mathematics, simplifying expressions often involves applying the rules of exponents. One common scenario is simplifying expressions like **(a^2)^3**. Let's break down how to do this:

### Understanding the Rules of Exponents

The key rule to remember here is the **power of a power rule**. This rule states that when raising a power to another power, you multiply the exponents.

Mathematically: **(a^m)^n = a^(m*n)**

### Applying the Rule

In our example, we have **(a^2)^3**. Applying the power of a power rule:

**(a^2)^3 = a^(2*3)****(a^2)^3 = a^6**

Therefore, the simplified form of **(a^2)^3** is **a^6**.

### Example:

Let's say a = 2. We can verify our simplification by plugging in the value:

**(a^2)^3 = (2^2)^3 = 4^3 = 64****a^6 = 2^6 = 64**

As we can see, both expressions result in the same answer, confirming our simplification.

### Key Takeaways:

**Power of a power rule:**(a^m)^n = a^(m*n)- Remember to multiply the exponents when simplifying expressions with nested powers.
- You can verify your simplification by plugging in a value for the variable.