%5E4.jpeg "(3x^2y^2)^4")
Simplifying (3x^2y^2)^4
In mathematics, simplifying expressions is a fundamental skill. Let's break down how to simplify the expression (3x^2y^2)^4.
Understanding the Power of a Power Rule
The key to solving this lies in the power of a power rule. This rule states that when raising a power to another power, you multiply the exponents.
In our case, we have a base of (3x^2y^2) raised to the power of 4.
Applying the Rule
Let's apply the power of a power rule:
- (3x^2y^2)^4 = 3^4 * (x^2)^4 * (y^2)^4
Now, we need to apply the power of a power rule again to the terms with exponents:
- 3^4 * (x^2)^4 * (y^2)^4 = 81 * x^(24) * y^(24)
Simplifying the Expression
Finally, we can simplify the expression to:
- 81 * x^(24) * y^(24) = 81x^8y^8
Conclusion
Therefore, the simplified form of (3x^2y^2)^4 is 81x^8y^8. This illustrates how understanding and applying the power of a power rule can help simplify complex expressions.