%5E2-simplify.jpeg "(2x^2y^3)^2 Simplify")
Simplifying (2x^2y^3)^2
This article will guide you through the process of simplifying the expression (2x^2y^3)^2.
Understanding the Power of a Product Rule
The key to simplifying this expression lies in understanding the power of a product rule:
(ab)^n = a^n * b^n
This rule tells us that when raising a product to a power, we can distribute the power to each factor in the product.
Applying the Rule
Let's apply the power of a product rule to our expression:
(2x^2y^3)^2 = 2^2 * (x^2)^2 * (y^3)^2
Simplifying Further
Now, we can simplify each individual term:
- 2^2 = 4
- (x^2)^2 = x^(2*2) = x^4
- (y^3)^2 = y^(3*2) = y^6
Final Result
Combining these simplified terms, we get our final simplified expression:
(2x^2y^3)^2 = 4x^4y^6
Summary
In summary, we have successfully simplified the expression (2x^2y^3)^2 by applying the power of a product rule and simplifying each individual term. The final simplified expression is 4x^4y^6.