## Understanding (u^4)^4

In mathematics, particularly in algebra, we often encounter expressions involving exponents raised to further exponents. One such expression is **(u^4)^4**. This might seem complex at first glance, but it follows a simple rule: **the power of a power rule**.

### The Power of a Power Rule

The power of a power rule states that when raising a power to another power, we **multiply the exponents**. This is represented mathematically as:

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

Applying this to our expression:

**(u^4)^4 = u^(4*4) = u^16**

### Simplifying the Expression

Therefore, **(u^4)^4** simplifies to **u^16**. This means that **u^4** is multiplied by itself four times, resulting in u raised to the power of 16.

### Example

Let's consider an example to illustrate this further. Assume **u = 2**:

**(u^4)^4 = (2^4)^4 = (16)^4 = 65536**

In this case, **(u^4)^4** evaluates to **65536**.

### Conclusion

Understanding the power of a power rule is essential for simplifying expressions involving exponents. Applying this rule allows us to efficiently simplify expressions like **(u^4)^4**, resulting in a more concise and manageable form.