%5E4.jpeg "(x^3y^2)^4")
Simplifying (x^3y^2)^4
In mathematics, simplifying expressions is a fundamental skill. One common type of simplification involves raising a power to another power. Let's break down the process of simplifying the expression (x^3y^2)^4.
Understanding the Rules
The key principle at play here is the power of a power rule:
(a^m)^n = a^(m*n)
This rule states that when raising a power to another power, we multiply the exponents.
Applying the Rule
Let's apply this rule to our expression:
(x^3y^2)^4 = x^(34) * y^(24)
This gives us:
(x^3y^2)^4 = x^12 * y^8
Final Result
Therefore, the simplified form of (x^3y^2)^4 is x^12 * y^8.
Summary
By applying the power of a power rule, we successfully simplified the expression (x^3y^2)^4 to x^12 * y^8. This process demonstrates the importance of understanding and applying mathematical rules for efficient simplification.