State the properties used in the following statements: `(76xx23)xx89=76xx(89xx23)`

Answer

To solve the question and state the properties used in the expression `(76 × 23) × 89 = 76 × (89 × 23)`, we will break it down step by step.

### Step-by-Step Solution:

1. **Identify the Expression**: The given expression is `(76 × 23) × 89 = 76 × (89 × 23)`.

2. **Understand the Operations**: We are dealing with multiplication in this expression.

3. **Recognize the Properties of Multiplication**:
- **Commutative Property**: This property states that changing the order of the numbers in multiplication does not change the product. For example, \( A × B = B × A \).
- **Associative Property**: This property states that the way in which numbers are grouped in multiplication does not change the product. For example, \( (A × B) × C = A × (B × C) \).

4. **Analyze the Given Expression**:
- The left side of the equation is `(76 × 23) × 89`.
- The right side of the equation is `76 × (89 × 23)`.

5. **Apply the Associative Property**:
- We can see that both sides of the equation can be rearranged without changing the result.
- The left side groups `76` and `23` first, while the right side groups `89` and `23` first.

6. **Conclusion**: Since the grouping of the numbers does not affect the result of the multiplication, we conclude that the property used in this expression is the **Associative Property of Multiplication**.

### Final Answer:
The property used in the statement `(76 × 23) × 89 = 76 × (89 × 23)` is the **Associative Property of Multiplication**.