%5E2-simplify.jpeg "(3x^2y^3)^2 Simplify")
Simplifying the Expression (3x^2y^3)^2
In this article, we will simplify the expression (3x^2y^3)^2. To do this, we will use the rules of exponents and the order of operations.
Step 1: Apply the Power of a Product Rule
The power of a product rule states that when we raise a product of two or more factors to a power, we can raise each factor to that power and then multiply the results. Mathematically, this can be represented as:
(ab)^n = a^n * b^n
In our case, we have:
(3x^2y^3)^2 = ?
Using the power of a product rule, we can rewrite this as:
(3x^2y^3)^2 = 3^2 * (x^2)^2 * (y^3)^2
Step 2: Simplify the Exponents
Next, we need to simplify the exponents. For 3^2, we have:
3^2 = 9
For (x^2)^2, we have:
(x^2)^2 = x^(2*2) = x^4
For (y^3)^2, we have:
(y^3)^2 = y^(3*2) = y^6
Step 3: Multiply the Results
Now, we can multiply the results together:
3^2 * (x^2)^2 * (y^3)^2 = 9 * x^4 * y^6
Therefore, the simplified expression for (3x^2y^3)^2 is:
(3x^2y^3)^2 = 9x^4y^6
And that's the final answer!
