## Simplifying Expressions with Exponents

In mathematics, we often encounter expressions involving exponents. These expressions can be simplified using various rules of exponents. Let's consider the expression:

**(xy^2)^3(x^2y^3)^3**

To simplify this expression, we'll use the following rules:

**Power of a Product:**(ab)^n = a^n * b^n**Power of a Power:**(a^m)^n = a^(m*n)

**Step 1: Apply the power of a product rule to each term.**

This gives us: (x^3 * y^6)(x^6 * y^9)

**Step 2: Apply the power of a power rule.**

This simplifies to: x^(3+6) * y^(6+9)

**Step 3: Combine the exponents.**

This leads to the final simplified expression:
**x^9 * y^15**

Therefore, the simplified form of (xy^2)^3(x^2y^3)^3 is **x^9y^15**.

**Key Takeaways:**

- Understanding the rules of exponents is crucial for simplifying complex expressions.
- By applying these rules step-by-step, we can systematically simplify expressions involving exponents.
- The simplified form of the expression is a more concise representation of the original expression.