(3ab^4)^4

less than a minute read Jun 16, 2024
(3ab^4)^4

Simplifying (3ab^4)^4

In mathematics, simplifying expressions is a key skill. Let's explore how to simplify the expression (3ab^4)^4.

Understanding the Rules

To simplify this expression, we need to understand two key rules of exponents:

  • Power of a Product: (xy)^n = x^n * y^n
  • Power of a Power: (x^m)^n = x^(m*n)

Applying the Rules

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

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

  3. Simplify the exponents: 3^4 * a^4 * b^(4*4) = 81a^4b^16

Final Result

Therefore, the simplified expression for (3ab^4)^4 is 81a^4b^16.

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