## Understanding (x^5)^4

In mathematics, when dealing with exponents, we often encounter expressions like (x^5)^4. This might seem confusing at first, but it's actually quite simple to understand.

### The Power of a Power Rule

The core concept here is the **power of a power rule**. This rule states:

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

In simpler terms, when you raise a power to another power, you multiply the exponents.

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

Let's apply this rule to our expression (x^5)^4:

**a = x****m = 5****n = 4**

Following the rule, we get:

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

Therefore, (x^5)^4 simplifies to **x^20**.

### Why This Works

The reason this rule works is because of the definition of exponents. Raising something to a power means multiplying it by itself a certain number of times.

For example, **x^5** means x multiplied by itself five times: x * x * x * x * x

When we raise **x^5** to the power of **4**, we are essentially multiplying **x^5** by itself four times:

(x^5)^4 = (x^5) * (x^5) * (x^5) * (x^5)

Expanding this, we get:

(x * x * x * x * x) * (x * x * x * x * x) * (x * x * x * x * x) * (x * x * x * x * x)

This results in x being multiplied by itself twenty times, which is represented by **x^20**.

### Conclusion

The power of a power rule is a fundamental concept in algebra. By understanding this rule, we can simplify complex expressions like (x^5)^4 and express them in a much more concise way.