## Simplifying the Expression (a^2b^3b)^4

The expression (a^2b^3b)^4 can be simplified using the rules of exponents. Here's a breakdown of the steps:

### 1. Combine Like Terms:

**b^3b**simplifies to**b^4**because when multiplying exponents with the same base, you add the powers.

The expression now becomes (a^2b^4)^4.

### 2. Apply the Power of a Product Rule:

**(ab)^n = a^n * b^n**This rule states that when raising a product to a power, you raise each factor to that power.

Applying this to our expression:

(a^2b^4)^4 = a^(2*4) * b^(4*4)

### 3. Simplify the Exponents:

- a^(2*4) = a^8
- b^(4*4) = b^16

The final simplified expression is **a^8b^16**.

### Summary:

By applying the rules of exponents, we can simplify the complex expression (a^2b^3b)^4 to a much simpler form: **a^8b^16**. This process demonstrates the importance of understanding exponent rules for efficient algebraic manipulation.