A Class-III student perform multiplication of `16 xx 25` as follows `16 xx 25 = 8 xx 2 xx 5 xx 5 = 8 xx 5 xx 2 xx 5 = 40 xx 10 = 400`
Which property of multiplication has the student used in this question?

Options

A. Inverse multiplication law
B. istributive law
C. Associative law
D. Repeated addition

Explanation

To determine the property of multiplication that the student used in their calculation of \(16 \times 25\), we can analyze the steps they took:

1. **Initial Multiplication**: The student started with the multiplication \(16 \times 25\).

2. **Breaking Down the Numbers**: The student rewrote \(16\) as \(8 \times 2\) and \(25\) as \(5 \times 5\). So, the expression became:
\[ 16 \times 25 = (8 \times 2) \times (5 \times 5) \]

3. **Rearranging the Factors**: The student then rearranged the factors:
\[ (8 \times 2) \times (5 \times 5) = 8 \times 5 \times 2 \times 5 \]

4. **Grouping the Factors**: Next, they grouped the factors for easier multiplication:
\[ (8 \times 5) \times (2 \times 5) \]

5. **Calculating the Products**: The student calculated:
\[ 8 \times 5 = 40 \quad \text{and} \quad 2 \times 5 = 10 \]
Then, they multiplied these results:
\[ 40 \times 10 = 400 \]

The final result is \(400\), which is indeed the correct answer for \(16 \times 25\).

### Conclusion
The student used the **Associative Property of Multiplication**, which states that the way in which numbers are grouped in multiplication does not change the product. In this case, they rearranged and grouped the factors without changing the final result.