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(3x4y2)4

less than a minute read Jun 16, 2024
(3x4y2)4

Simplifying (3x^4y^2)^4

This expression involves both exponents and parentheses, so we need to use the rules of exponents to simplify it.

Rule of Exponents

The key rule we'll use is: (a^m)^n = a^(m*n). This means when you have a power raised to another power, you multiply the exponents.

Applying the Rule

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

  1. Distribute the outer exponent:
    (3x^4y^2)^4 = 3^4 * (x^4)^4 * (y^2)^4

  2. Simplify each term: 3^4 = 81 (x^4)^4 = x^(44) = x^16 (y^2)^4 = y^(24) = y^8

  3. Combine the terms: 81 * x^16 * y^8 = 81x^16y^8

Final Answer

Therefore, the simplified form of (3x^4y^2)^4 is 81x^16y^8.

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