Which of the following expressions is equivalent to (x^3 * y^2)^2?

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Question: Which of the following expressions is equivalent to (x^3 * y^2)^2?

Options:

Correct Answer: x^6 * y^4

Solution:

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

Which of the following expressions is equivalent to (x^3 * y^2)^2?

Which of the following expressions is equivalent to (x^3 * y^2)^2?

Step 1: Identify the expression we need to simplify, which is (x^3 * y^2)^2.
Step 2: Recognize that we can use the power of a product rule, which states that (a * b)^n = a^n * b^n.
Step 3: Apply the power of a product rule to our expression: (x^3 * y^2)^2 becomes x^3^2 * y^2^2.
Step 4: Simplify x^3^2 by multiplying the exponents: 3 * 2 = 6, so we have x^6.
Step 5: Simplify y^2^2 by multiplying the exponents: 2 * 2 = 4, so we have y^4.
Step 6: Combine the results from Step 4 and Step 5 to get the final expression: x^6 * y^4.

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