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

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

Options:

Correct Answer: x^4y^6

Solution:

Using the power of a power property, we multiply the exponents: (x^2)^2 = x^4 and (y^3)^2 = y^6.

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

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

Step 1: Identify the expression we need to simplify, which is (x^2y^3)^2.
Step 2: Use the power of a power property, which states that when you raise a power to another power, you multiply the exponents.
Step 3: Apply this property to x^2. Since we have (x^2)^2, we multiply the exponents: 2 * 2 = 4. So, (x^2)^2 = x^4.
Step 4: Now apply the same property to y^3. We have (y^3)^2, so we multiply the exponents: 3 * 2 = 6. Thus, (y^3)^2 = y^6.
Step 5: Combine the results from Step 3 and Step 4. We get (x^2y^3)^2 = x^4y^6.

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