## Simplifying (5x^4)^3

This expression involves both **exponents** and **parentheses**. To simplify it, we need to apply the rules of exponents:

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

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

Let's break down the simplification step-by-step:

**(5x^4)^3 = 5^3 * (x^4)^3** (Applying the power of a product rule)

**(5x^4)^3 = 125 * x^(4*3)** (Applying the power of a power rule)

**(5x^4)^3 = 125x^12**

Therefore, the simplified form of (5x^4)^3 is **125x^12**.

**Key Takeaways:**

- Remember the order of operations (PEMDAS/BODMAS) when dealing with expressions involving exponents and parentheses.
- Understanding the rules of exponents is essential for simplifying complex expressions.
- Applying these rules systematically allows you to simplify expressions efficiently.