%5E3-simplify.jpeg "(5x^4)^3 Simplify")
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.