Which of the following is the correct simplification of (x^3 * y^2)^(2)?

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Question: Which of the following is the correct simplification of (x^3 * y^2)^(2)?

Options:

Correct Answer: x^6 * y^4

Solution:

Using the power of a product property, (a*b)^n = a^n * b^n, we get (x^3)^2 * (y^2)^2 = x^6 * y^4.

Which of the following is the correct simplification of (x^3 * y^2)^(2)?

Which of the following is the correct simplification of (x^3 * y^2)^(2)?

Step 1: Identify the expression to simplify, which is (x^3 * y^2)^(2).
Step 2: Use the power of a product property, which states that (a * b)^n = a^n * b^n.
Step 3: Apply this property to the expression: (x^3 * y^2)^(2) becomes (x^3)^(2) * (y^2)^(2).
Step 4: Simplify (x^3)^(2) using the power of a power property, which states that (a^m)^n = a^(m*n). This gives us x^(3*2) = x^6.
Step 5: Simplify (y^2)^(2) in the same way: (y^2)^(2) gives us y^(2*2) = y^4.
Step 6: Combine the results from Step 4 and Step 5 to get the final simplified expression: x^6 * y^4.

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