State the properties used in the following statements: `234xx(456xx54)=(234xx456)xx54`

Answer

To solve the question, we need to identify the properties used in the statement:

**Statement:** \( 234 \times (456 \times 54) = (234 \times 456) \times 54 \)

### Step-by-Step Solution:

1. **Understanding the Expression:**
The expression consists of three numbers being multiplied: 234, 456, and 54. The multiplication is grouped differently on both sides of the equation.

2. **Identify the Properties:**
- The left side of the equation is \( 234 \times (456 \times 54) \).
- The right side of the equation is \( (234 \times 456) \times 54 \).

3. **Recognizing the Associative Property:**
- The associative property of multiplication states that the way in which numbers are grouped in multiplication does not change the product. In mathematical terms, it can be expressed as:
\[ a \times (b \times c) = (a \times b) \times c \]
- Here, if we let \( a = 234 \), \( b = 456 \), and \( c = 54 \), we can see that both sides of the equation are structured according to this property.

4. **Conclusion:**
Therefore, the property used in the statement \( 234 \times (456 \times 54) = (234 \times 456) \times 54 \) is the **Associative Property of Multiplication**.

### Final Answer:
The property used is the **Associative Property of Multiplication**.

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