(3x^4)^2 Simplify

Jasonbradley

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Jun 16, 2024

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Simplifying (3x^4)^2

In mathematics, simplifying expressions often involves applying the rules of exponents. Let's break down how to simplify the expression (3x^4)^2.

Understanding the Rules of Exponents

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

Applying the Rules

1. Apply the Power of a Product rule:
   (3x^4)^2 = 3^2 * (x^4)^2

2. Apply the Power of a Power rule: 3^2 * (x^4)^2 = 9 * x^(4*2)

3. Simplify: 9 * x^(4*2) = 9x^8

Conclusion

Therefore, the simplified form of (3x^4)^2 is 9x^8. By understanding the rules of exponents and applying them systematically, we can simplify complex expressions efficiently.