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

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

Options:

Correct Answer: x^6y^4

Solution:

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

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

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

Step 1: Identify the expression you need to simplify, which is (x^3y^2)^2.
Step 2: Use the power of a product property, which states that (ab)^n = a^n * b^n.
Step 3: Apply this property to the expression: (x^3y^2)^2 becomes (x^3)^2 * (y^2)^2.
Step 4: Simplify (x^3)^2 by multiplying the exponent: 3 * 2 = 6, so (x^3)^2 = x^6.
Step 5: Simplify (y^2)^2 by multiplying the exponent: 2 * 2 = 4, so (y^2)^2 = y^4.
Step 6: Combine the results from Step 4 and Step 5: x^6 * y^4.
Step 7: Write the final simplified expression: x^6y^4.

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