(3x^4)^2 Simplify

less than a minute read Jun 16, 2024
(3x^4)^2 Simplify

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.

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