## Understanding (x^2y^3)^4

This expression involves **exponents** and **power of a product**. Let's break it down step-by-step.

### Exponents Explained

**Base:**The base is the number or variable being multiplied by itself. In this case, the bases are**x**and**y**.**Exponent:**The exponent tells you how many times to multiply the base by itself. Here, we have**2**and**3**as exponents for**x**and**y**, respectively.**Power:**The entire expression (x^2y^3) is raised to the power of**4**. This means we are multiplying the entire expression by itself four times.

### Applying the Rules

To simplify this, we use the following rules:

**1. Power of a Product:** When raising a product to a power, you raise each factor to that power.

- (x^2y^3)^4 = (x^2)^4 * (y^3)^4

**2. Power of a Power:** When raising a power to another power, you multiply the exponents.

- (x^2)^4 = x^(2*4) = x^8
- (y^3)^4 = y^(3*4) = y^12

**Therefore, the simplified expression is:**

**(x^2y^3)^4 = x^8y^12**

### In Conclusion

Simplifying (x^2y^3)^4 is a straightforward process using the basic rules of exponents. By applying the power of a product and power of a power rules, we arrive at the simplified form x^8y^12.