## Understanding (a^5)^4

In mathematics, **(a^5)^4** represents a power raised to another power. This expression can be simplified using the **power of a power rule**. This rule states that when raising a power to another power, you multiply the exponents.

### The Power of a Power Rule

The power of a power rule is expressed as:

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

This means that when you have a base (a) raised to a power (m), and then that entire expression is raised to another power (n), you can simplify it by multiplying the exponents (m and n).

### Applying the Rule to (a^5)^4

In our example, we have (a^5)^4. Applying the power of a power rule, we get:

**(a^5)^4 = a^(5*4) = a^20**

Therefore, **(a^5)^4 is equivalent to a^20**.

### Example

Let's say **a = 2**. Using the simplified expression, we can calculate the result:

**a^20 = 2^20 = 1,048,576**

This demonstrates how simplifying the expression using the power of a power rule can be helpful for calculations.

### Summary

In summary, **(a^5)^4** can be simplified to **a^20** using the power of a power rule. This rule is a fundamental concept in algebra and helps to simplify complex expressions involving exponents.