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

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

Options:

Correct Answer: x^(3-2) * y^(2-1)

Solution:

Using the property of exponents for division, we subtract the exponents: x^(3-2) * y^(2-1) = x^1 * y^1.

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

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

Step 1: Write down the expression you want to simplify: (x^3 * y^2) / (x^2 * y).
Step 2: Identify the parts of the expression: the numerator is x^3 * y^2 and the denominator is x^2 * y.
Step 3: Use the property of exponents for division, which says to subtract the exponents of the same base.
Step 4: For the x terms, subtract the exponent in the denominator from the exponent in the numerator: 3 - 2 = 1. So, x^3 / x^2 = x^1.
Step 5: For the y terms, subtract the exponent in the denominator from the exponent in the numerator: 2 - 1 = 1. So, y^2 / y = y^1.
Step 6: Combine the results from Step 4 and Step 5: x^1 * y^1.
Step 7: Write the final simplified expression: x * y.

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