(ab)^4

2 min read Jun 16, 2024

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.