%5E4.jpeg "(3x^4y^2)^4")
Simplifying (3x^4y^2)^4
In mathematics, simplifying expressions often involves applying the rules of exponents. One such expression is (3x^4y^2)^4. Let's break down how to simplify it.
Understanding the Rules of Exponents
The key rule we'll use here is the power of a product rule. This states that when raising a product to a power, we raise each factor to that power:
(ab)^n = a^n * b^n
Applying the Rule
- Distribute the exponent: We apply the power of a product rule to our expression:
(3x^4y^2)^4 = 3^4 * (x^4)^4 * (y^2)^4
- Simplify each term:
- 3^4 = 81
- (x^4)^4 = x^(4*4) = x^16
- (y^2)^4 = y^(2*4) = y^8
- 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.