## Understanding (ab^2)^3

In mathematics, simplifying expressions like (ab^2)^3 involves applying the rules of exponents. Here's a breakdown of how to approach this:

### The Power of a Product Rule

The **power of a product rule** states that when raising a product to a power, we raise each factor to that power:

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

### Applying the Rule

Let's apply this rule to our expression (ab^2)^3:

**Identify the factors:**In this case, we have two factors: 'a' and 'b^2'.**Raise each factor to the power of 3:**- a^3
- (b^2)^3

**Simplify the second factor:**We apply the**power of a power rule**which states (x^m)^n = x^(m*n)- (b^2)^3 = b^(2*3) = b^6

### The Final Result

Therefore, the simplified expression for (ab^2)^3 is:

**a^3 * b^6**

This process illustrates how understanding the rules of exponents allows us to simplify complex expressions and manipulate them efficiently.