## Understanding (a^2b^3)^2

The expression (a^2b^3)^2 is a simple example of how exponents work with multiple variables. Let's break down the components and learn how to simplify it.

### Understanding the Components

**a^2:**This represents 'a' multiplied by itself twice (a * a).**b^3:**This represents 'b' multiplied by itself three times (b * b * b).**( )^2:**This indicates that the entire expression inside the parentheses is being squared, meaning it's being multiplied by itself.

### Simplifying the Expression

To simplify (a^2b^3)^2, we can apply the following rules:

**Exponent Rule:**When raising a power to another power, we multiply the exponents.**Distributive Property:**The exponent applies to each individual factor within the parentheses.

Applying these rules, we get:

**(a^2b^3)^2 = (a^2)^2 * (b^3)^2**

Now, applying the exponent rule:

**(a^2)^2 * (b^3)^2 = a^(2 2) * b^(32)**

Finally, simplifying the exponents:

**a^(2 2) * b^(32) = a^4 * b^6**

### Final Result

Therefore, the simplified form of (a^2b^3)^2 is **a^4b^6**.

### Key Points

- The exponent rule is crucial for simplifying expressions with exponents raised to other exponents.
- Remember to apply the exponent to each factor within the parentheses.
- This simplification process is applicable to any similar expressions involving multiple variables and exponents.