## Understanding (ab)^4

In mathematics, **(ab)^4** represents the **fourth power of the product of two variables, 'a' and 'b'**. This expression can be simplified using the rules of exponents.

### Expanding the Expression

Here's how to expand the expression:

**(ab)^4 = (ab) * (ab) * (ab) * (ab)**

Since multiplication is commutative and associative, we can rearrange the terms:

**(ab)^4 = a * a * a * a * b * b * b * b**

This simplifies to:

**(ab)^4 = a^4 * b^4**

### Key Takeaways

**(ab)^4 is equivalent to a^4 * b^4**.- This means that raising a product to a power is the same as raising each factor to that power and then multiplying the results.
- This rule applies to any number of factors and any exponent.

### Example

Let's consider an example:

- If a = 2 and b = 3, then:
- (ab)^4 = (2 * 3)^4 = 6^4 = 1296
- a^4 * b^4 = 2^4 * 3^4 = 16 * 81 = 1296

As you can see, both methods lead to the same result.

### Conclusion

Understanding how to simplify expressions like (ab)^4 is crucial in algebra and other mathematical fields. By applying the rules of exponents, we can break down complex expressions into simpler ones, making calculations easier and more efficient.