%5E2.jpeg "(4a^3b^2)^2")
Simplifying (4a^3b^2)^2
In mathematics, simplifying expressions often involves applying rules of exponents. One such rule states that when raising a product to a power, we raise each factor to that power. Let's apply this to the expression (4a^3b^2)^2.
Breaking Down the Expression
- Understanding the Power of a Product Rule: (xy)^n = x^n * y^n
- Applying the Rule: (4a^3b^2)^2 = 4^2 * (a^3)^2 * (b^2)^2
Simplifying Further
- Simplifying Powers of Numbers: 4^2 = 16
- Simplifying Powers of Variables:
- (a^3)^2 = a^(3*2) = a^6
- (b^2)^2 = b^(2*2) = b^4
The Final Result
Therefore, the simplified form of (4a^3b^2)^2 is 16a^6b^4.